Dynamic atomic reconstruction: how Fe3O4 thin films evade polar catastrophe for epitaxy

Polar catastrophe at the interface of oxide materials with strongly correlated electrons has triggered a flurry of new research activities. The expectations are that the design of such advanced interfaces will become a powerful route to engineer devices with novel functionalities. Here we investigate the initial stages of growth and the electronic structure of the spintronic Fe3O4/MgO (001) interface. Using soft x-ray absorption spectroscopy we have discovered that the so-called A-sites are completely missing in the first Fe3O4 monolayer. This allows us to develop an unexpected but elegant growth principle in which during deposition the Fe atoms are constantly on the move to solve the divergent electrostatic potential problem, thereby ensuring epitaxy and stoichiometry at the same time. This growth principle provides a new perspective for the design of interfaces.

one may want to design: interfaces which appear impossible to grow at first sight may now be tried out.
Here, we investigate the polar interface between Fe3O4 and the MgO (001) substrate, one of the most used interfaces in the research field of spintronics. [16][17][18][19][20][21][22][23][24] This interface is completely not understood in terms of atomic structure, electronic structure and growth mode.  (001) is also known to produce films with excellent physical properties [22]. In order to obtain direct insight into the atomic and electronic structure of the interface, we utilize soft x-ray absorption spectroscopy (XAS) at the Fe L2,3 edges. This spectroscopic technique is extremely sensitive to the local coordination and charge state of the Fe ions [25][26][27][28].
Fe3O4 thin films with thicknesses varying between 0.67 and 8 monolayers (ML) were grown on MgO (001). Each film has been grown on a new and freshly annealed substrate. The substrate temperature was kept at 250 °C during the growth in order to avoid the Mg inter-diffusion at the Fe3O4/MgO interface [29,30]. Details about the film growth are given in the Supplementary Materials [31]. One ML consists of one (001)-oriented layer of oxygen anions together with the appropriate number of Fe cations to maintain charge neutrality and stoichiometry, and has a thickness of 2.1 Å . In Fig. 1 (c), and (d) we present representative reflection high energy electron diffraction (RHEED) and low energy electron diffraction (LEED) patterns, respectively, of a 200 nm thick Fe3O4 film to demonstrate that the surface is still smooth for very long deposition times.
The typical �√2 × √2�R45° surface reconstruction is also clearly visible. Fig. 1 (e) shows the regular oscillations with time in the intensity of the specularly reflected RHEED beam during growth, indicating a two-dimensional layer-by-layer growth mode. Fig. 1 (f) Fig. S1]. We also include in Fig. 2 the spectra of bulk YBaCo3FeO7 [28], bulk FeO (reproduced from Ref. 32) and bulk Fe2O3 as references for Fe 3+ ions in tetrahedral coordination, Fe 2+ ions in octahedral coordination, and Fe 3+ ions in octahedral coordination, respectively. The line shapes of the spectra strongly depend on the multiplet structure given by the atomic like Fe 3d-3d and 2p-3d Coulomb and exchange interactions, as well as by local crystal fields and the hybridization with the O 2p ligands [25][26][27][28]. Here we note the striking similarities of the spectral features of the 8 ML Fe3O4 thin film and the bulk magnetite, which confirms that our Fe3O4 films have the correct stoichiometry.
We now focus on the thickness dependence of the spectra. Clear and systematic changes can be observed, in particular in the peak position of the spectral feature labeled as (I) and in the intensity of the spectral feature labeled as (II) relative to that of peak (I), see Fig. 2. The position of peak (I) of the thinnest Fe3O4 films, i.e. of the 0.67, 0.75 and 1 ML films, is the same as that of bulk Fe2O3, while for the thicker films, i.e. 2 ML and beyond, it is more similar to that of bulk YBaCo3FeO7. This gives a first indication that the thinnest films contain only tiny amounts of Fe 3+ ions in tetrahedral coordination and implies that such A-site Fe ions could essentially only be present for films of 2 ML thickness and beyond. This then would also explain why for the thinnest films one can see two separate peaks (I) and (II) like in bulk Fe2O3 (green curve), while for thicker films the appearance of an in-between peak associated with the Fe 3+ ions in tetrahedral coordination (red curve) will fill up the valley between peak (I) and (II), making peak (II) to become a shoulder and the position of the larger peak (I) to shift to lower energies. Important is to note that the foot at the onset of the Fe L3 edge, i.e. the feature between 706 and 707.7 eV, which is part of the spectral feature characteristic for Fe 2+ ions in octahedral B sites (see blue curve), are thickness independent. All these strongly suggest that the spectral weight of the A-site and the B-site Fe 3+ ions varies strongly with thickness.
To interpret and better understand the XAS spectra and their thickness dependence we have performed calculations using the well established configuration interaction cluster model that includes the full atomic multiplet theory and the local effects of the solid [25][26][27][28]. We have simulated each of the XAS spectra shown in Fig. 2  where the error bars reflect the deviations of the fits to the experimental data. From the relative concentrations of the constituents we have calculated the average valence or equivalently, by taking the oxygen lattice to be complete, we have determined the Fe content y in our FeyO films.
These y values are plotted as black closed squares in the bottom panel of Fig. 3. We can observe that all points are very close to the Fe3/4O (gray) line, which confirms the correct stoichiometry of our films through the entire thickness range and very consistent with the RHEED intensity oscillations which have a constant time period, i.e. independent of the film thickness.
An important aspect that emerges directly from the simulations is the strong thickness dependence of the different Fe constituents, see Fig. 3. We recall that bulk Fe3O4 has 1/3 (33%) Fe 3+ ions in tetrahedral coordination (A-sites), 1/3 (33%) Fe 2+ and 1/3 (33%) Fe 3+ ions in octahedral coordination (B-sites). We found to our surprise that the amount of A-site Fe 3+ ions is practically negligible for the thinnest films, i.e. 2-3% instead of the 33% bulk value. At the same time, the amount of B-site Fe 3+ in the thinnest films is between 60-68%, much larger than the 33% bulk value. We also observe that with increasing film thickness the A-site Fe 3+ amount increases and the B-site Fe 3+ decreases, both to approach the 33% bulk value, see for example the 8 ML results in Fig. 3. Interestingly, the amount of B-site Fe 2+ is rather constant and independent of the film thickness, it fluctuates around the 33% bulk value.
These spectroscopic findings provide crucial data for the determination of the actual growth process and the interface structure. Especially the observation that the first monolayer of the Fe3O4 film has essentially no A-sites is a surprising piece of information. In fact, as far as the monolayer is concerned, the choice of 'nature' not to have A-sites is the simplest manner to solve the planar electrostatic potential problem. As can be seen from Figs. 1 (a) and (b), it is indeed the presence of the A-sites that causes the polar catastrophe to occur as there are no negative ions in those A-site planes to neutralize the charges. So by not having A sites for the first monolayer, there is also no electrostatic problem. What we then have is that the first monolayer constitutes basically of a charge-neutral non-polar rocksalt FeO layer with 25% Fe vacancies. All Fe ions are occupying the B-site with 33% of them having the 2+ valence and 67% the 3+ state and the vacancies are not ordered since we did not observe any superstructure. We have also carried out polarization dependent XAS measurements, and we are able to indeed verify in detail that also the dichroic spectrum is consistent with the 33% Fe 2+  For the second monolayer, we observe in the experiment the appearance of some amount of A-sites, about 16.7%, see top panel of Fig. 3. We now can arrive at the following model, see Fig.   4 where the left panel shows the growth process and the right panels the corresponding net charges, electric field, and electric potential of each plane. Since in bulk magnetite, a monolayer per unit cell includes 2 A-site Fe 3+ , 2 B-site Fe 2+ , 2 B-site Fe 3+ , and 8 oxygen ions, we will use the formula notation Fe6O8 instead of Fe3/4O to describe each monolayer. When deposited, the second monolayer will first form a non-polar monolayer, like the first monolayer. Then, both the first and the second layers give away one Fe 3+ ion as shown in Fig. 4  For a 3-ML film, the layer added will again form a non-polar monolayer first. This monolayer and the subsurface monolayer then carry out the same process in which both give away one Fe 3+ ion to the space in between. See Fig. 4 (c). Again, the potential divergence remains nullified after this process as shown on the most right panel of Fig. 4 (c). One complete bulk Fe6O8 layer now is formed. This growth process is repeated for the subsequent layers, and the model predicts that the concentration of the A-site ions will increase following the geometrical series 2(n-1)/6n, while the concentration of the Fe 2+ B-site ions will remain constant at 2n/6n = 33% and that of the Fe 3+ B-site ions will decrease following 2(n+1)/6n, where n denotes the number of monolayers. These predictions of the model are also presented in Fig. 3. We can see that the essential behavior observed in the experiment is well reproduced with convergence to the bulk values for thicker films. We also would like to note that an ordering in the outer Fe5O8 layer can be made consistent with the often observed �√2 × √2�R45° surface reconstruction in thicker (001) Fe3O4 films, please see the Supplementary Materials for details [31].
We thus have found that the A-sites are absent in the first monolayer or interface, and that Fe ions are on the move while the films is growing to accommodate for the presence of A-sites inside the film having the proper crystal structure and stoichiometry. We clearly have a 'dynamic atomic reconstruction' taking place here.
It is interesting to note that the Fe3O4 thin films are insulating and that the interface does not induce metallicity as shown by the resistivity measurements displayed in Fig. 1 (f). This is obviously in contrast with the resistivity measurements on SrTiO3/LaAlO3 [5,[35][36][37] and SrTiO3/RETiO3 [13][14][15]. In principle, the Fe5O8 interface layer could have been conducting since this layer can be considered as a defective and doped rocksalt FeO layer. Yet, considering the fact that small polaron effects in bulk Fe3O4 are strong and hamper the conductivity [38][39][40], we may expect that this will also be the case for the interface layer. Its resistivity will then be dominated by strong scattering effects due to disorder.
Our findings have direct and important implications for the field of Fe3O4 spintronics. There are some reports concerning the possible existence of a magnetically dead layer at the interface [41][42][43], but others ascribe the decrease of the magnetization in the thin films to the presence of antiphase boundaries leading to superparamagnetic behavior of the domains [44][45][46]. Our findings may give credit to the proponents of the dead magnetic layer model. In view of the absence or low amount of A-sites in the interface region, some of the superexchange paths which determine the ferrimagnetism in Fe3O4 are certainly missing. This then would also explain why tunneling experiments have spin-polarizations different than expected from the properties of bulk Fe3O4 [47]. We now can propose that the insertion of a monolayer of magnetic metals like Fe, Co, Ni, or even noble metals like Cu, Ag, Au or Pt between the Fe3O4 and the insulating oxide substrate will drastically change the situation: the metal layer inserted will act as a charge reservoir that can accommodate the flow of planar charges required to stabilize a Fe3O4 interface layer which has A-sites like in the bulk. The occurrence of a magnetically dead layer can then be prevented and also the spin polarization at the interface may be increased. A hint that the latter is not unrealistic can be found in an early work by Dedkov et al. [48] on oxidized Fe films deposited on metal substrates.
To summarize, using soft x-ray absorption spectroscopy we find that nature provides us with an unexpected but elegant solution for the polar catastrophe problem at the Fe3O4/MgO (001) interface: the A-site Fe 3+ ions are missing in the first Fe3O4 layer and the growth process involves movements of not only the surface but also the subsurface Fe ions, securing epitaxy and stoichiometry at the same time. Having identified this 'dynamic atomic reconstruction' growth principle, we conclude that we really have to think differently and openly about how polar interfaces can grow. Apparently, 'nature' offers us a much wider range of opportunities to prepare unstable polar interfaces. It would be interesting to put effort to grow a monolayer or a few monolayer of Fe3O4 film where the defects are ordered, so that diffraction techniques can confirm the growth model.     Fig. S1 shows the full Fe L2,3 XAS spectra of the Fe3O4 films together with the spectra of bulk Fe3O4, bulk YBaCo3FeO7 (Fe 3+ in tetrahedral coordination) [1], bulk FeO (Fe 2+ in octahedral coordination) [2] and bulk Fe2O3 (Fe 3+ in octahedral coordination): the spectra are identical to those in Figure 2 in the main text, but with a wider photon energy window covering both Fe L3 and L2 edges.
Configuration interaction cluster calculation. To interpret and better understand the x-ray absorption (XAS) spectra and their thickness dependence we have performed simulations using the well established configuration interaction cluster model that includes the full atomic multiplet theory and the local effects of the solid [3][4][5]. It accounts for the intra-atomic Fe 3d-3d and 2p-3d Coulomb and exchange interactions, the atomic 2p and 3d spin-orbit couplings, the O 2p-Fe 3d hybridization and the local ionic crystal field. The calculations were done using the program XTLS 8.3 [5]. The XAS spectra of Fe3O4 can be decomposed into the three sub-spectra of the three Fe sites, i.e. A-site Fe 3+ , B-site Fe 2+ , and B-site Fe 3+ . We have considered an FeO4 and an FeO6 cluster for each Fe A-site and B-site, respectively. Parameters for the multipole part of the Coulomb interactions were given by 75% and 80% of the Hartree-Fock values for the d−d and p−d Slater integrals, respectively, while the monopole parts (Udd, Ucd) as well as the O 2p-Fe 3d charge transfer energy (∆) were adopted from typical values for Fe 2+ and Fe 3+ ions [6,7]. The hopping integrals between the Fe 3d and O 2p were calculated for the various Fe-O bond lengths according to Harrison's description [8]. The Fe-O bond lengths were taken from x-ray singlecrystal structure diffraction data [9]. The crystal field parameter 10Dq was tuned to fit the experimental spectra. All parameters are listed in Ref. 10. The relative energy positions for the three sub-spectra were determined in such a way that the simulated total MCD spectrum fits by the experimental MCD spectrum best, see Refs. 6, 11, and 12. The fits were done using the "NMimimize" function of the Mathematica software [13].
By making weighted sums with the three isotropic sub-spectra using the "NMimimize" function of the Mathematica software [13] to obtain the best fit to the experimental spectrum of each Fe film with the different thicknesses, we extract the relative amount of B-site Fe 2+ , A-site Fe 3+ , and B-site Fe 3+ ions as a function of film thickness. The XAS simulation results of the Fe3O4 thin films of 0.67, 0.75, 1, 1.5, 2, 3, 4, 5, 6, and 8 MLs are shown in Fig. S3.
To double check the validity of the three isotropic sub-spectra, we compare them in Figure S4 with the experimental XAS spectra of the standard references for each Fe site, i.e., bulk YBaCo3FeO7 [1] for the A-site Fe 3+ , bulk FeO [2] for the B-site Fe 2+ , and bulk Fe2O3 for the B-site Fe 3+ (same as those shown in Figure 2 in the main text, and in Figure S1 in the supplementary materials). Each of them reproduces the experimental spectrum of its corresponding reference very well. We include also in Figure S4 the XAS spectrum from Fe0.04Mg0.96O [14], a system of Fe impurities embedded in MgO. The identical spectral features of the bulk FeO and of the Fe impurity system clearly demonstrate that XAS is most sensitive to the presence of the nearest neighbor ligands only. We have also done calculations for an Fe 2+ in FeO5 and an Fe 3+ in FeO5 by simply removing the apical oxygen of the FeO6, but otherwise using the same parameters as those for FeO6, as shown in Figure S4. Only minor differences can be observed between the isotropic XAS spectra of an Fe 2+ in FeO6 and in FeO5, and of an Fe 3+ in FeO6 and FeO5. The large difference between the isotropic XAS spectra of octahedral Fe 3+ and tetrahedral Fe 3+ originates from the fact that the effective 10Dq ligand/crystal field value is positive for the octahedral coordination while it is negative for the tetrahedral coordination.
1 ML Fe3O4 thin film: polarization dependence. Figure S5 shows the experimental linear polarization-dependent Fe L2,3 XAS spectra of the 1 ML Fe3O4. In the bottom panel, the experimental linear dichroic (LD) signal, defined as the difference between two polarizations (E || C -E ⊥ C) is displayed, together with the calculated LD spectrum for the scenario of 33 % B-site Fe 2+ and 67 % B-site Fe 3+ . The LD signal can be well reproduced without including any contribution from the A-site Fe 3+ ion. All this can be very well understood: the isotropic spectrum is determined mostly by the octahedral part of the ligand/crystal field, while the dichroism is due to the small tetragonal part of the crystal field in the monolayer. This tetragonal part of the crystal field makes the orbital occupation of the high-spin d 6 ion to become anisotropic, resulting in the polarization dependence of the intensity of the Fe 2+ signal. The tetragonal part of the crystal field does not affect the orbital occupation of the spherical high-spin d 5 ion but sets up the energy splitting in the XAS final states, resulting in the polarization dependence of the Fe 3+ peak position.
Please note that these XAS spectra and the dichroism therein are very different from those of Fe atoms on MgO [15], confirming the notion that L2,3-XAS is indeed an extremely powerful method to determine the local electronic structure of transition metal systems.
1 ML Fe3O4 thin film capped with 10 ML MgO. Fig. S6 shows the Fe L2,3-XAS spectra of the 1 ML Fe3O4 film, the 1 ML Fe3O4 film capped with 10 ML MgO, and the Fe0.04Mg0.96O system [14]. One can clearly observe that the spectrum of the 1 ML Fe3O4 changes drastically upon capping with MgO and that the spectrum becomes identical to that of octahedral Fe 2+ in