Fe3O4 thin films: controlling and manipulating an elusive quantum material

Fe3O4 (magnetite) is one of the most elusive quantum materials and at the same time one of the most studied transition metal oxide materials for thin film applications. The theoretically expected half-metallic behavior generates high expectations that it can be used in spintronic devices. Yet, despite the tremendous amount of work devoted to preparing thin films, the enigmatic first order metal-insulator transition and the hall mark of magnetite known as the Verwey transition, is in thin films extremely broad and occurs at substantially lower temperatures as compared to that in high quality bulk single crystals. Here we have succeeded in finding and making a particular class of substrates that allows the growth of magnetite thin films with the Verwey transition as sharp as in the bulk. Moreover, we are now able to tune the transition temperature and, using tensile strain, increase it to substantially higher values than in the bulk.

While thousands of studies have been devoted to try to understand the first order Verwey transition in magnetite, the high Curie temperature (T C ∼ 860 K) and the half-metallic character of Fe 3 O 4 as predicted by band theory [1,2] have triggered considerable research efforts world wide to make this material suitable for spintronic applications in the form of thin film devices [3,4,5,6,7]. Using a variety of deposition methods, epitaxial growth on a number of substrates has been achieved [5,6,7,8]. Yet, it is remarkable that in the twenty years of research on Fe 3 O 4 thin films, the first order Verwey transition [9] in thin films is always broad [6,7,10,11,12,13].
While in the bulk the transition takes place well within 1 K, the reported resistivity curves for the thin films showed transition widths of about 10 K or more. The Verwey transition temperature T V in thin films is also much lower, with reported values ranging from 100 to 120 K [6,7,10,11,12,13] while the stoichiometric bulk has T V of 124 K.
It has been reported that several factors can affect negatively the Verwey transition in bulk magnetite, such as oxygen off-stoichiometry [14] and cation substitution [15]. The T V gradually decreases and the transition is claimed to change from a first order to a second or even higher order with increasing oxygen off-stoichiometry or cation substitution. Recently, we have carried out a systematic study on the influence of oxygen stoichiometry for the properties of magnetite thin films [16], and we found that even for the optimal oxygen composition the transition remains broad. In that study, we also discovered that the microstructure of the films play an important role. In particular, with the films having a distribution of domain sizes, a larger spread of the distribution results in a broader transition and a small domain size gives lower transition temperatures. The transition itself is still first order since it shows hysteresis, and there are indications that each domain has its own transition temperature [16]. Various substrates have been used in the literature to grow epitaxial Fe 3 O 4 thin films, e.g. MgO, MgAl 2 O 4 , Al 2 O 3 , SrTiO 3 , and BaTiO 3 [6,7,10,11,12,13,16]. These studies may suggest that the larger the lattice mismatch, the broader the transition and the lower the average transition temperature [16].
Here we have succeeded in finding and making a particular class of substrates that allows the growth of magnetite thin films with the Verwey transition as sharp as in the bulk. The key principle is to obtain thin films with sufficiently large domains and small domain size distribution. Moreover, using tensile strain we now are able to increase the transition temperature to considerably higher values than that of the bulk. The occurrence of the Verwey transition in the highly anisotropic strained films raises a new question to the intricacies of the interplay between the charge and orbital degrees of freedom of the Fe ions in magnetite, adding another aspect of the elusiveness of this quantum material.

Results
In our quest for substrates that allow for the growth of Fe 3 O 4 thin films with large domains and a narrow distribution of domain sizes, we aim first of all for substrates with a very small lattice mismatch. Although MgO is ideal in this respect, the occurrence of anti-phase boundaries [11], which cannot be avoided when growing a (inverse) spinel film on a rocksalt substrate, has a negative effect on the distribution and size of the domains [16]. We therefore restrict ourselves to substrates with the spinel structure. We have identified Co 2 TiO 4 with a lattice mismatch of +0.66% as a potential candidate, and managed to prepare large single crystals of this compound using a mirror furnace. Substrates with ≈ 6 mm × 6 mm epi-polished surfaces have been made out of these crystals. We have also prepared crystals and substrates with somewhat larger lattice mismatch, up to +1.11 %, by partial substitution of the Co with Mn and/or Fe:   In fact we would like to note that films as thin as 10 nm grown on Co 1.75 Mn 0.25 TiO 4 (001) (+0.98%) and Co 1.25 Fe 0.5 Mn 0.25 TiO 4 (001) (+1.11%) have a T V + which is already comparable to that of the bulk, a highly remarkable result in view of the generally low values even for thicker films known in the literature [6,7,10,11,12,13,16].
We now investigate the strain state of the Fe 3 O 4 films grown on the spinel substrates using x-ray diffraction (XRD). Figure 3 presents the reciprocal space mapping of the (115) We can also get an insight about the microstructure of the films by analyzing the peak profile of the rocking curves of the (115) reflection. From the inverse of the peak width, we can estimate that the average domain size is about 46 nm, 61 nm, and 68 nm for the 40 nm film grown on the three spinel substrates, respectively. These numbers are higher than the 30 nm value found for an equivalent thick film grown on MgO [16], suggesting that the spinel structure of the substrate indeed does help to obtain films of structurally better quality. These results therefore support our conjecture that one needs films with sufficiently large domains and sufficiently narrow distribution of domain sizes in order to obtain sharp first order transitions.
one has to carefully design substrates with a matching lattice structure and sufficiently small lattice mismatch.

Discussion
Having achieved magnetite thin films with a Verwey transition as sharp as the bulk, we now are ready to meaningfully measure and analyze the effect of the strain exerted by the substrate on the transition of the film. It has been reported that the Verwey transition of bulk magnetite becomes broad and that T V drops linearly with increasing applied hydrostatic pressure and corresponding decrease of the unit cell volume [24,25,26,27]. While the application of negative hydrostatic pressures is experimentally out of reach, our finding that the T V of the Fe 3 O 4 thin films increases when epitaxially grown with increasing unit cell volume indicates that we have in fact succeeded to exert effectively negative pressures on magnetite by using the tensile strain imposed by the carefully chosen spinel substrates. Viewing the Verwey transition as a transition from a Wigner crystal to a Wigner glass of small polarons [28], one can readily accept that changing the one-electron band width, and therefore also the polaron band width, will alter the transition temperature [29]. In particular, enlarging the lattice constant and inter-atomic distances will facilitate the formation of an ordered state in which the different lattice sites have different local valence and orbital states.
Yet it is important to note that the negative pressures exerted on these thin films are by no means isotropic and therefore cannot be considered as being the equivalent of negative hydrostatic pressures. On the contrary, the films are expanded in the plane but compressed along the c-axis direction. This makes the Verwey transition in the tensile strained films even more interesting: would the charge and orbital order be of the same type as in the bulk, for which there is a lot of debate, see Refs. [30], [31], [32], and references therein. In this respect, we would like to note that the resistivity across the Verwey transition changes by about a factor 10 in the         Figure S1. Rietveld refinement results of powder X-ray diffraction measurements of our Co 2−x−y Fe y Mn x TiO 4 crystals (obtained from single crystals crushed to powder). As indicated by the difference line (Iobs-Icalc), there are no impurity phases in our single crystals. Some minor background problems are artificial observations within our powder X-ray diffraction measurements originating from the measurement configuration and not intrinsically from our sample (around 20  Figure S2. a, X-ray scattering intensities of Co 2 TiO 4 within the HK0 plane of reciprocal space. Obviously, our sample is a single phase single crystal without any other crystallites. b, Visualization of the crystal structure derived from our single crystal X-ray diffraction measurements of Co 2 TiO 4 . Red/blue spheres: Co-/O-ions; green spheres: 50% Co-ions and 50% Ti-ions.