Pulsed laser deposition films from a Ba₂FeMoO₆ target onto SrTiO₃[001]: Chemical and magnetic inhomogeneity

This paper focuses on Ba₂FeMoO₆ (BFMO) films, as BFMO is a magnetoresistive half-metal that retains this function at room temperature because the magnetic ordering temperature (T_C) can be as high as 367 K.¹ Half-metal ferromagnets like BFMO are of theoretical interest and also have clear application potential in magneto-optics and spintronics.² Moreover, polycrystalline ceramics of BFMO have reported magnetoresistances of greater than 30%.^3,4 For incorporation in devices, thin films are required, and BFMO films have reduced T_C and saturation magnetization (M_SAT) compared to polycrystalline samples.⁵ The lack of explanation for the observed differences between BFMO films on SrTiO₃ (STO) and BFMO powders is a hard limit to applications of BFMO and is the impetus of this work.

More broadly, BFMO is a double perovskite (DP) of the Elpasolite⁶ motif for which the general formula is written as A₂BB′O₆ and consists of two interpenetrating perovskite (ABO₃/AB′O₃) sublattices, whereby there is a three dimensional chemical ordering of the B and B′ species that doubles the ≈4 Å, perovskite unit cell in all three Cartesian directions. By utilizing a combination of 3d and 4d or 5d ions on the B/B′ sites, DPs can have contributions of itinerant and localized magnetism. Aside from BFMO, DPs may present unusual magnetotransport, ferroelectric, and magnetic properties that expand upon the already diverse perovskite materials.⁷ 

The BFMO is similar to the more intensely studied Sr₂FeMoO₆ (SFMO) that boasts a higher T_C = 420 K, but a smaller magnetoresistance.⁸ The SFMO sparked interest because of the room temperature magnetoresistance, and the translation to thin film geometries shows a strong potential for device applications.⁹ The naïve estimate of M_SAT = 4 μ_B/f.u. for antiparallel alignment of more localized Fe³⁺ (5 μ_B) and more itinerant Mo⁵⁺ (1 μ_B) in these materials is never fully achieved in polycrystals due to the defects and the breakdown of this simple picture,¹⁰ and both T_C and M_SAT are typically less in thin films compared to polycrystals.^11,12 Two defects that may be present in DPs are anti-site, whereby the chemical order of B and B′ is imperfect and off-stoichiometry of the B and B′ sites (A₂B_1+xB′_1−xO₆ where x=[0,1]).^13,14 In addition, the usual off-stoichiometry possible in perovskites, quantified typically by oxygen content,¹⁵ may also affect the behavior of DPs.

Aside from synthesis subtleties, films may be subject to strain at the interface with the substrate due to lattice mismatches. Polarized neutron reflectometry (PNR) is useful to probe the magnetization depth profile and search for correlations with interface effects.¹⁶ Previously, PNR has been used to understand the strain-induced interface effects in the DP Sr₂CrReO₆ (SCRO).¹⁷ Here, we apply PNR to the BFMO thin films. For the BFMO films on SrTiO₃ (STO) via pulsed laser deposition (PLD), there is a strange feature whereby there is a clear inflection point in the magnetization at around 250 K, which gives rise to M_SAT = 1.2 μ_B for the optimal growth condition, but above this putative T_C, there is still a ferromagnetic response at 300 K that has M_SAT = 0.4 μ_B for the optimized growth condition.⁵ One hypothesis of this study is that there may be different magnetic contributions as a function of depth in the BFMO target films deposited on STO (BFMO//STO) that may be probed by PNR.

Following this introduction, the technical details are described in Sec. II. Section III presents our results of X-ray diffraction (XRD), atomic force microscopy (AFM), X-ray reflectivity (XRR), PNR, and X-ray photoelectron spectroscopy (XPS). These results are discussed in Sec. IV to generate a model of the magnetism and stoichiometry in the PLD BFMO//STO and summarized in the concluding Sec. V.

Films were deposited following the reported procedure of PLD for Ba₂FeMoO₆ on SrTiO₃,⁵ with a variation in the repetition rate and total time in order to tune the film thickness. Four films were prepared for this report, with identifiers assigned as per Table I.

The XPS was collected on a Kratos AXIS Ultra DLD spectrometer equipped with a monochromatic Al source (1486.6 eV) operating at 140 W under a vacuum of 1 × 10⁻⁸ Torr. Survey scans were used for better signal to noise when quantifying elemental compositions, and region scans were used for higher resolution to quantify peak splittings. In region scans, the pass energy of the analyzer was set at 20 eV using an energy step size of 0.05 eV, while survey scans used an analyzer pass energy of 160 eV with a step size of 1 eV. The C 1s peak of the adventitious carbon was set to 284.8 eV as a point of reference. Relative sensitivity factors provided with the instrument were used for elemental analysis. Shirley backgrounds were used, and peaks were fit to pseudo-Voigt functions.

Specular XRD experiments were performed on a Rigaku Ultima III Analytical X-Ray Diffractometer with a 2θ/θ design from 2θ = 10° to 150° using a copper anode. This XRD setup has Cu-K_α1 (λ = 1.5406 Å) and Cu-K_α2 (λ = 1.5444 Å) radiations, with the typical Cu-_Kα satellite (λ = 1.5345 Å) as well as a contamination of W-L_α (λ = 1.4704 Å).^18,19 The off-specular XRD reciprocal space maps were measured with a Bruker D8 Advance diffractometer using a copper anode.

AFM of films was scanned using an Asylum Cypher High Resolution Atomic Force Microscope multimode scanning probe microscope with the tapping mode. The images were quantified with the Gwyddion software.²⁰ 

XRR experiments were performed on a Bruker D8 Advance diffractometer using a copper anode and a Sol-X detector. Specular reflectivity data were taken with the detector angle equal to the incident beam angle and an attenuator was used for positions near and below the critical edge when the reflected intensity was at maximum.

PNR was performed on the PBR (λ = 4.75 Å) and the MAGIK (λ = 5.00 Å) reflectometers at the NIST Center for Neutron Research.²¹ The magnetic field of 0.8 T is in the plane of the film.

XRR and PNR data were reduced to a reflectivity profile and corrected for the footprint using reflred in the reflpak suite.²² Profile fitting was performed using the Refl1D software package, with the DREAM and differential evolution algorithms that attempt to avoid local minima in parameter space.²³ The fitting algorithm in Refl1D, by way of a Monte Carlo Markov-Chain based optimization, allows for parameter uncertainty estimation via the standard deviation (σ_STD) of the tested cases, and n = 1000 test cases were used in all fits. For reference, 1σ_STD is the 68% confidence interval, 1.96σ_STD is the 96% confidence level, and 2.58σ_STD is the 99% confidence level. For fit comparison of the magnetic contribution, a parameter to track the uncertainty in the spin-asymmetry U_SA = Σ(|SA_obs-SA_calc|)/Σ|SA_obs| is used, where SA is the spin asymmetry. Due to the many orders of magnitude over which the reflectivity varies, and the nuclear and magnetic contributions for PNR, χ² is less sensitive to the details of the magnetic model. Throughout, the momentum transfer Qz is normal to the plane of the film.

XRD was used to probe the crystallinity of the BFMO and to extract unit cell parameters of films i, ii, iii, and iv. XRD with the momentum transfer perpendicular to the plane of the film showed intense beams from the 00 L peaks of the STO substrate, with significantly smaller BFMO peaks on the lower-angle, larger-d-spacing side. The most intense BFMO peak is that related to the STO 002, shown in Fig. 1(a). This peak was seen to increase in intensity with deposition cycles while changing the spacing between B and B′ double perovskite sites d_BB′, Table II. The precision of the x-ray diffractometer is estimated to be better than 10⁻⁴, while a deconvolution of the resolution function of the instrument suggests an additional broadening in the films due to either finite size or strain. Peak positions were found by least squares fitting of Gaussian functions with fitting uncertainties less than ±0.0004 Å for the peak center. For films i and ii, Laue oscillations were observed (ΔQ = 2π/Na for “N” repeats of a crystallographic plane distance “a”), while iii and iv are presumed to be too thick to observe such oscillations due to the limited resolution of the diffractometer used. By comparing the different momenta of the fringes, the crystalline thicknesses of i and ii were estimated to be 20 nm and 60 nm, respectively. The BFMO peak that is analogous to the STO 002 was further investigated via a reciprocal space map that is displayed for i in Fig. 1(b).

AFM was used to reveal the surface features of the films i, ii, iii, and iv. The initial image processing involved leveling by mean plane subtraction, aligning rows with a median method, and shifting the minimum height value to zero. These data are visualized as one-dimensional line-scans that integrate the vertical direction, as divided into four 1.25 μm regions, in Figs. 2(a) and 2(d) and as two-dimensional heat maps in Figs. 2(e)–2(h). Three types of features are seen in Fig. 2: (1) a wavy and connected surface characterized by the lateral coherence length (ξ) and surface roughness (σ), (2) small particulates on the surface that are characterized by their equivalent diameter (d_particle) and relative area compared to the total image area (A_particle), and (3) large chunks. Inflection points were seen in the height distribution function due to the surface particulates, with values of 5.5 nm, 6.4 nm, 12.3 nm, and 15.2 nm, and due to the surface chunks, with values of 8.4 nm, 9.3 nm, 15.9 nm, and 18.8 nm, for films i, ii, iii, and iv, respectively. A height-height-correlation-function (HHCF)²⁴ that is a function of the lateral distance, r, was used to quantify the lateral coherence length, using a Gaussian such that

where the maximum value of r was taken at 1 μm for fitting. The HHCF was calculated with thresholding to remove the contribution of the surface particles (to give σ, ξ), and without thresholding to remove the contribution of the surface particles (to give σ*, ξ*). The threshold cutoff was determined by manual inspection of the height profiles to remove the localized spikes due to surface particles or chunks. The analysis of the thresholded particulates was used to extract d_particle and A_particle. The results of these fittings are summarized in Table III. The large chunks did not occur frequently enough to allow quantitative analysis, but were typically in the range of 50 nm to 200 nm, and for the limited sampling available, they increased in size with film thickness.

XRR can determine the macroscopic interface parameters and depth dependent chemical composition via the scattering length densities that are probed through interactions of the X-rays with electrons. XRR shows the expected behavior of a total reflectance critical angle followed by a sharp decay at higher momentum transfers. For films i and ii, Kiesseg fringes are observed (ΔQ = 2π/d for a film of thickness “d”), while iii and iv are presumed too thick to observe such oscillations due to a limit of the resolution for this instrument, Fig. 3. The bare STO substrate was also measured, but is not shown. A rocking curve at finite momentum transfer shows the central specular peak and two diffuse scattering Yoneda wings that are characteristic of in-plane roughness and appear at positions, where the source or detector angle with respect to the sample surface equals the critical angle, as shown in the inset of Fig. 3. Films i and ii could be fit well with a single slab model to extract a film thickness, scattering length density (SLD), and roughness. Films iii and iv could not extract a thickness due to the absence of observable fringes, but scattering length density and roughness parameters could be extracted. The long period wave-vector discrepancies between experiments and fits could be reduced with additional model layers at the surface, but at the expense of additional parameters that may be masking subtleties of the background. For the STO substrate, the roughness could be fit to give a value of 0.6 nm. The results of the fits are shown in Table IV.

PNR is sensitive to depth dependent nuclear composition and net magnetization perpendicular to the momentum transfer. The PNR was collected for the two films, i and ii that are of a thickness appropriate to the probe. Four cross sections were measured, R₊₊, R₋₋, R₊₋, and R₋₊, where the first two are non-spin-flip events, the second two are spin-flip events, and the sign symbols denote the neutron polarization directions. The spin-flip events, which are sensitive to magnetization orthogonal to the applied magnetic field that is in the plane of the film, were found to be negligible for these samples in this setup. For sample i, data were collected at 300 K and at 110 K, where 110 K was chosen, because it is above the structural phase transition of STO that can cause surface rumpling.²⁵ For sample ii, data were collected at 300 K and 110 K in a lower resolution and higher flux mode, and an additional 300 K data set was measured in a higher resolution and lower flux mode. Both samples i and ii show a splitting of the R₊₊ and R₋₋ cross sections that is due to net magnetization, and which is represented by the existence of spin asymmetry, SA = (R₊₊ − R₋₋)/(R₊₊ + R₋₋), Figs. 4 and 5.

The simplest model for these data would be a mono-slab on the STO, and there is an approximate reproduction of the data for both films, Figs. 4 and 5. Some mono-slab fit parameters are shown in Table V.

For sample i, the crossing of R₊₊ and R₋₋ (zero crossing in the SA) cannot be reproduced with a homogeneous depth profile as for a mono-slab, but instead requires a different length scale for the nuclear and magnetic scattering. Tellingly, a tri-slab model allowing for magnetic and compositional changes at the interfaces may be refined to generate a zero crossing in the SA. In fact, the zero crossing is possible with a mono-slab nuclear scattering length density profile and a tri-slab magnetic scattering length density profile, but subtle changes in the nuclear part improve the fit. Additional layers beyond the tri-slab could subtly improve the model, but at the expense of overparameterization and model instability. For sample ii, the mono-slab model also has shortcomings in the reproduction of the magnetic scattering, but more qualitative features are reproduced than for i. The more complex tri-slab model whereby additional slabs at the STO to film and film to air interface are included is more quantitatively accurate for sample ii as well. The goodness of fit parameters of the various models and experimental conditions are summarized in Table VI. For both i and ii, it is found that there is larger magnetic scattering length density in the region of the STO to film interface that decreases toward the film to air interface. As the samples are cooled, the magnetization increases throughout the sample, but with a smaller increase near the surface than in the rest of the film. The thickness of the more magnetic phase is ≈10 nm, and for sample i it is ≈7 nm, while for sample ii, the relaxation is more gradual with an inflection closer to 20 nm. For sample i, the tri-slab model also shows a gradient in the nuclear scattering length density that is larger at the STO interface and decreases toward the air interface with a strong correlation to the magnetic phase. Such a chemical gradient is not required for the XRR data, which may be due to an increased sensitivity of the neutron experimental parameters or imply that the assertion of a chemical gradient is weak. For sample ii, the data are not sufficient to definitively make a statement on a potential nuclear scattering length gradient. Some tri-slab fit parameters are shown in Table VII.

XPS is a surface sensitive probe of chemical species, and films i, ii, iii, and iv were all measured. Survey and region scans are described in Sec. II. The degree of surface sensitivity may be estimated by considering the inelastic mean free path, which is calculated using the TPP-2M equation²⁶ and is shown in Fig. 6(a) for Ba₂FeMoO₆. These mean free path estimations suggest that even from the thinnest film, sample i, the substrate is not probed. Survey scans, Fig. 6(b), were used to investigate the elemental composition, but the extracted values will be modulated by the surface concentrations and efficiency of the electron scattering process for a given moiety. Nevertheless, all observed peaks could be assigned and the extracted elemental signals from Ba 3d, Sr 3d, Fe 2p, O 1s, and Mo 3d are shown in Table VIII. As anticipated, Ba, Fe, Mo, and O are all present, as is adventitious carbon, and in addition, Sr is present at the surface, while Ti is absent. Region scans were performed to further investigate the ions, Figs. 6(c)–6(f), and Ba 3d, O 1s, and Mo 3d all show two distinct species (Ba₁, Ba₂, O₁, O₂, Mo₁, Mo₂), while Fe 2p only shows on species within the experimental resolution (Fe). Within the uncertainty, the expected branching ratios were observed, and the peak positions are shown in Table IX.

Data have been presented in the Sec. III that shows the BFMO//STO films studied possess a degree of heterogeneity, which is not surprising given that the impetus of this work was to better understand the two magnetic ordering temperatures (T_C,1 > 300K and T_C,2 ≈ 240 K) reported for similarly prepared samples of BFMO//STO.⁵ The higher magnetic density region near the STO interface may be assigned to the T_C,1 > 300 K transition, while the lower magnetic density region near the air interface may be assigned to the T_C,2 ≈ 240 K transition. In the following, we attempt to unify the data to describe the surface features, the chemical characteristics of the film, and the magnetic characteristics of the film.

These BFMO//STO films are mainly crystalline. The XRD showed a pseudo-perovskite phase that has an elongated lattice constant out of the plane that increases with film thickness, and previous work on films by the same group under identical growth conditions have shown registered epitaxy.⁵ The changing lattice constant with film thickness suggests a depth dependent strain in the films. The Laue and Kiessig fringes gave similar thicknesses for the films thin enough to resolve (i and ii), showing that the preponderance of the film is one crystalline structure. No extra phases were seen with XRD, which means that any additional possible phases would be a significantly lesser volume and likely randomly oriented, whereby the diffracted beams are less concentrated in the solid angle. Grossly, the XPS of i, ii, iii, and iv all showed that there are Sr, Ba, Fe, Mo, and O present at the surface of the films. Sr is not present in the target and must diffuse from the substrate to the film during PLD. This type of A-site mixing of film and substrate has been seen in PLD of SrRuO₃ and Pr_0.7Ca_0.3MnO₃²⁷ and LaCrO₃ on SrTiO₃.²⁸ 

There are surface features on these films. AFM shows a connected film of nanometer roughness (as does reflectivity) that is coated by hundred nanometer chunks and tens of nanometer particulates. The surface sensitive XPS showed at least two chemical species being present for Ba, O, and Mo. Therefore, it is likely that the surface objects belong to a different crystal structure than the surface of the crystalline film that leaves the two phases immiscible. At higher oxygen pressures than used here, BaMoO₄ was seen in XRD of BFMO//STO,⁵ and SrMoO₄ was seen in XRD of SFMO//STO.²⁹ Fe₃O₄ and elemental Fe were also observed in SFMO//STO XRD for higher vacuum environments.²⁹ While BaMoO₄ is not observed in the XRD of i, ii, iii, and iv, there is evidence for its presence in the XPS. BaMoO₄ is reported to have Ba²⁺3d_5/2 = 779.1 eV, Mo⁶⁺3d_5/2 = 232.2 eV, and O²⁻1s = 531.0 eV,³⁰ which are respectively near Ba₁ or Ba₂, Mo₁, and O₂, respectively. The Mo₂ peak would then correspond to Mo⁵⁺ as in BFMO. The O₁ = 529.7 eV O1s signal is a perovskite peak that is present in CaTiO₃ and BaTiO₃ (BTO), and the BTO peak for Ba3d_5/2 = 779.0 eV is near Ba₁ and Ba₂.³¹ 

The data show a non-trivial chemical make-up in the crystalline film phase. Previously, BFMO//STO chemical analysis by energy-dispersive X-ray spectroscopy on a scanning tunneling electron microscope did not identify off-stoichiometry of Mo:Fe from 1 : 1, but no quantities were reported, and the temperature dependence of the resistivity in that report⁵ was consistent with an Fe-rich material.⁷ Similarly, for a study of SFMO//STO, no off-stoichiometry of the B-site was identified, but no quantities were reported.²⁹ For the film phase, the reflectivity studies provide chemical information. The neutron and X-ray scattering lengths arise from different interactions and therefore the potential for different elemental contrast, which is achieved in this instance, Table X. Using the unit cell parameters from XRD, a connection between chemical formula and scattering length density is possible. For a formula of Ba₂FeMoO₆, ρ_N,neutron = 4.99 × 10⁻⁶ Å⁻² and ρ_X-ray = 51.78 × 10⁻⁶ Å⁻² (for sample i unit cell parameters) and experimentally for sample i, ρ_N,neutron = 5.118 × 10⁻⁶ Å⁻² at the STO interface, ρ_N,neutron = 4.04 × 10⁻⁶ Å⁻² at the air interface, and ρ_X-ray = 46.12 × 10⁻⁶ Å⁻², while for sample ii, ρ_N,neutron = 4.933 × 10⁻⁶ Å⁻² and ρ_X-ray = 46.46 × 10⁻⁶ Å⁻². Qualitatively, the undershooting of ρ_X-ray compared to that expected for pure BFMO suggests that Fe and Sr are likely richer than the ideal case, and similar arguments can be made for the relative values of ρ_N,neutron. Quantitatively, taking a chemical formula parameterized with three variables of Sr_2-yBa_yFe_1+xMo_1-xO_6-z, it is possible to co-fit the chemical formula to the experimentally determined ρ_N,neutron and ρ_X-ray. At the STO interface, these fits give Ba_0.98Sr_1.02Fe_1.29Mo_0.71O_5.78 for film i and Ba_1.14Sr_0.86Fe_1.19Mo_0.81O_5.48 for film ii. At the film surface, the sample ii data did not refine a different SLD for these data, while the data point at the terminal surface for sample i gives Ba_2.00Sr_0.00Fe_1.40Mo_0.60O_3.81 but the meaning of such numbers within the experimental uncertainty is unclear. Similarly, normalizing the XPS to the two A-sites yields Sr_1.18Ba_0.82, Sr_1.35Ba_0.65, Sr_1.26Ba_0.74, and Sr_1.22Ba_0.78, while for the B-sites, a similar scaling gives Fe_1.31Mo_0.69, Fe_1.38Mo_0.62, Fe_1.32Mo_0.68, and Fe_1.64Mo_0.36 for films i, ii, iii, and iv, respectively. The strontium present in XPS at the surface in film i seems to suggest that the films have a degree of chemical homogeneity and strontium leeches through the entire film i. Along these lines, the similar XPS derived surface strontium concentrations for films that are 17 nm (as determined from reflectivity for sample i) and up to ≈300 nm (as estimated from XRD intensity and number of deposition cycles for sample iv) suggest an approximately uniform strontium concentration throughout, although there may be a subtler concentration gradient that is beyond these data. The XRD unit cell parameters may also give some insight into the chemical formula in a less quantitative way. One potential issue when attempting to use XRD as an elemental analyst for BFMO is the multiple oxidation states that may be present and change with stoichiometry. For example, BFMO is considered to be Ba₂²⁺Fe³⁺Mo⁵⁺O₆²⁻, and if the end members are Ba²⁺Fe⁴⁺O₃²⁻ (a_BaFeO3 = 3.971 ų²) and Ba²⁺Mo⁴⁺O₃²⁻ (a_BaMoO3 = 4.040 ų³), then the oxidation states must change on the transition metals for different stoichiometries that will in turn affect the bond lengths. Qualitatively, x > 0 (y < 0) will reduce the unit cell volume and x < 0 (y > 0) will increase the unit cell volume. Oxygen off-stoichiometry may reduce the unit cell volume in both cases, as oxygen rich formulas are typically realized as A-site vacancies.¹⁵ In SFMO deposited via PLD, such a deficiency of the alkaline earth metal was seen.²⁹ Alternatively, for the isoelectronic A-site substitution in Sr_yBa_1-yFeMoO₆, Vegard's law of averages is expected to approximately hold as in Sr_yBa_1-yMoO₃³³ and Sr_yBa_2-yFeMoO₆.³⁴ The cube-root of the single-perovskite unit cell volumes (V) of i, ii, iii, and iv may be calculated using the a_STO = 3.90 Å for the in-plane lattice constants and the out-of-plane lattice constants in Table II to yield V_i^1/3 = 3.943 Å, V_ii^1/3 = 3.944 Å, V_iii^1/3 = 3.947 Å, and V_iv^1/3 = 3.946 Å, respectively. For BFMO, V_BFMO^1/3 = 4.031 Å, which is significantly larger than the V_STO^1/3 = 3.90 ų⁵ of the substrate, resulting in an even worse match than for SFMO//STO, as V_SFMO^1/3 = 3.949 Å.¹ For y ≈ 1, as in the reflectivity fits, V_y≈1^1/3 = 3.990 Å, and from the Fe doping experiments on SFMO, there would also be a decrease in lattice parameter for x > 0.³⁶ In the synthesis paper of BFMO//STO, it was found that increasing the growth temperature from 600 °C to 900 °C (in 100 °C increments) monotonically decreased the out of plane lattice constant,⁵ suggesting that there may be an annealing toward a ground state with a smaller film unit cell volume. Here, the out of plane lattice constant generally increases with thickness, although the repetition rate of the laser also changes, so it is unclear which effect might dominate, but in both cases, this would suggest that in the vicinity of the substrate, there is a tendency to have a reduced lattice constant. These interfacial lattice constant considerations illustrate a possible force driving the Sr to Ba and Mo to Fe chemical concentrations.

Just as the film may be affected by the substrate, the film deposition may also induce changes in the surface of the substrate at the interface. We have presented evidence that the source of the strontium that is diffused to the deposited films, from a Ba₂FeMoO₆ target, must be from the SrTiO₃ substrate. This cation diffusion of strontium into the PLD films that SrTiO₃ may transform to Sr_αBa_βTiO₃ near the interface. Previously, we referenced the cubic a_STO = 3.90 Å, and while the BTO is tetragonal at room temperature (a = 3.9998 Å, c = 4.0180 Å), the a_BTO = 4.006 Å pseudo-cubic lattice parameter may be used to compare and is more than 2% larger than a_STO. Diffusion of the alkaline earth metal cations across the interface into the substrate would reduce the strain between substrate and deposited film, and there are data consistent with such a process. The XRR and PNR data may be considered in the context of a more complex model that allows a substrate interface layer; such complex models may be problematic due to the potential for non-uniqueness. The XRR fits presented in Sec. III C are robust to give the mono-slab thickness with a well determined parameter set. Due to the length scales probed, this effect of a discrete substrate surface modification is clearest in sample i. A new model (mono-slab*) includes an additional slab at the substrate to film interface and an additional slab at the film to air interface, Fig. S1 in the supplementary material. For the mono-slab model, χ² = 4.62, and this is decreased to χ² = 1.30 in the mono-slab* model. The additional slab at the film to air interface has no appreciable effect, while the slab at the substrate to film interface refines to a thickness of 2.92 ± 0.03 nm, with an SLD of 42.95 ± 0.05 × 10⁻⁶ Å⁻². For reference, the SLD of STO is 39.7 × 10⁻⁶ Å⁻² and the SLD of BTO is 44.4 × 10⁻⁶ Å⁻², as calculated from their crystallographic parameters,^35,37 where the dominant factor in these different SLDs is due to the number of electrons, and a secondary factor is the lattice constants changing. The mono-slab* model film has an SLD of 44.73 ± 0.03 × 10⁻⁶ Å⁻² (versus 46.12 ± 0.17 × 10⁻⁶ Å⁻² for the mono model). A similar complexification is possible for the PNR tri-slab model, to have a tri-slab* model that allows for the substrate STO to change SLD as an additional parameter. These PNR tri-slab* fits tend toward 3.2 × 10⁻⁶ Å⁻² at the film to STO interface, which is between 3.5 × 10⁻⁶ Å⁻² for STO and 3.0 × 10⁻⁶ Å⁻² for BTO, and the resulting magnetic profiles are changed by less than 10% for such a modification.

The magnetism in the films is inhomogeneous and may be connected to structural and chemical inhomogeneity. To put these BFMO//STO films in the context of the literature, the ρ_M magnetic scattering length density may be converted to μ_B by using the lattice constants determined with XRD and the magnetic scattering amplitude for one μ_B, p_MAG = 2.695 fm,³⁸ Table XI. For double-perovskites in general, the dominant factor reducing the net magnetic moment is typically the anti-site defects, whereby Mo and Fe sites here would swap, and the saturation magnetization (M_SAT) is approximately linear in the chemical order parameter without affecting T_C,¹³ but other factors may contribute. The observation of Sr in the films suggests that A-site doping may play a role in the magnetic response. One study of Sr_2-yBa_yFeMoO₆ using solid state synthesis found a non-linear, monotonic interpolation of T_C's between 420 K for y = 0 and 300 K for y = 2, with M_SAT measured at 80 K linearly varying between 2.1 μ_B/f.u. (f.u. = the double perovskite formula unit) for y = 0 and 3.0 μ_B/f.u. for y = 2.³⁴ A similar dependence of T_C upon Ba/Sr content was seen in a study of magnetocaloric effects in Sr doped Ba₂FeMoO₆.³⁹ Another report found an enhancement of the T_C of Sr_2-yBa_yFeMoO₆ for y = 0.4, before a decrease in T_C was observed,⁴⁰ and still another study found that there was no effect on T_C for up to y = 1.0, after which the T_C increased,⁴¹ and in both studies, M_SAT also increased with barium content. So, the Sr enrichment can increase T_C, but is not expected to alter the M_SAT. Conversely, iron doping up to x = 0.25 (the maximum reported) was found to have little to no effect on T_C, but linearly decreased M_SAT from 3.3 μ_B/f.u. at x = 0 to 2.3 μ_B/f.u. at x = 0.25.³⁶ Oxygen deficiency, as is seen here in the scattering length density model calculations, is expected for the low oxygen partial pressures used during synthesis, and for SFMO a decrease of 7% oxygen in the formula unit decreased M_SAT from 3.57 μ_B/f.u. to 3.30 μ_B/f.u., accompanied by subtle change in lattice constants (shrinking c but growing a to have <0.1% volume increase).⁴² For a phase to have T_C ≈ 240 K as in the BFMO//STO films near the surface, it is then most likely that finite size effects and grains come into play, and these microstructural effects would also affect the M_SAT for that region. Indeed, the AFM showed lateral structural coherence lengths at the surface to be ≈60 nm for films i, ii, iii, and iv, and a 5% barium doping of sol-gel synthesized Sr₂FeReO₆ found a reduction in M_SAT (by a factor of ≈3) and T_C as the grain sizes were reduced from 80–800 nm for the undoped with a wide distribution to 80–180 nm for the 5% barium doped with a tight distribution near 120 nm.⁴³ Additional work will be required if quantitative microstructural models are to be applied to this system. Finally, while there may be interface effects due to magnetic proximity,⁴⁴ these films seem to have their magnetic inhomogeneity connected to chemical and structural effects.

This section has made attempts to extract chemical and magnetic inhomogeneities by invoking a suite of probes, resulting in an array of extracted numbers. The possibility of unknown and systemic experimental uncertainties may limit quantitative comparison of these numbers. Some examples of uncertainties are that the scattering length density calculations are subject to changes in electron density and lattice constant changes (both of which may vary in the films in ways beyond the ability of these probes to interrogate), that the XPS relative sensitivity factors may be modified in the film matrix, as compared to the standards, that the sampling of microscopes like AFM may not be macroscopic in scope, and that subtle alignments can affect the scattering probes. On the other hand, there is a clear consistency to the results that have been discussed in this section.

In summary, we have presented data that progress the understanding of differences between BFMO powders and BFMO films on STO substrates. The out-of-plane lattice constant of BFMO//STO via XRD increases with film thickness from 4.040 Å for i (17 nm thick) to 4.034 Å for ii (74 nm thick) to 4.044 Å for iii (≈200 nm thick), and then decreases to 4.041 Å for iv (≈300 nm to ≈400 nm thick) versus 3.90 Å for STO and 4.031 Å for powder BFMO. Films i and ii that are appropriate for PNR have a region of higher T_C and M_SAT near the substrate interface (up to 7 nm and 20 nm from the interface, respectively) compared to the rest of the film and this temperature dependent magnetic depth profile explains the reported SQUID magnetometry observation of T_C,1 > 300 K and T_C,2 ≈ 240 K. Strontium of similar concentrations that is not present in the BFMO deposition target and Fe/Mo > 1 is observed via XPS within nanometers of the surface for all films, while neutron and X-ray reflectivity in concert for i and ii show similar strontium uptake and Fe/Mo > 1 at the STO interface. Two Ba and O species are observed in XPS within nanometers of the surface, where one is from the double-perovskite and the other from a BaMoO₄ phase, and this BaMoO₄ may be present as the particulates observed in the AFM. The lateral structural coherence length via AFM is ≈60 nm for all films at the surface.

And so, a semi-quantitative unified picture of BFMO//STO emerges that explains the previously puzzling decreased character of the magnetization measurements that suppressed M_SAT and had a majority phase of T_C (<T_C,powder) = 240 K. BaMoO₄ may precipitate out during PLD, leaving some remnants at the film surface as particulates and causing a Ba and Mo deficiency in the epitaxial film. The observation of Sr in the films was surprising, may help explain the non-monotonic magnetoresistance previously observed in BFMO//STO, and will be important to consider for similar (double) perovskites where a strain is present that may be relaxed via interstitial cation diffusion from the substrate. Within 10 nm to 20 nm of the STO interface where larger T_C and M_SAT is observed, the substrate may stabilize larger structural coherence lengths than the observed surface grains that may subdue T_C and M_SAT, but no data are available to quantify that aspect. The changing lattice constant with thickness suggests a depth dependent strain in the films, which has a lesser known effect. Iron richness, anti-site disorder, and oxygen vacancies may also conspire to affect the properties. These considerations will be essential to inform substrate choice in future BFMO applications.

See supplementary material for an XRR model including an additional substrate parameter.

The authors gratefully acknowledge the Summer Undergraduate Research Fellowship at the National Institute of Standards and Technology (NIST) Center for Neutron Research for Lisa J. Krayer, the financial support provided by NIST and the Center for High Resolution Neutron Scattering, and the usage of facilities supported, in part, by the National Science Foundation under Agreement No. DMR-0944772. Daniel M. Pajerowski is supported through the Scientific User Facilities Division of the Department of Energy (DOE) Office of Science, sponsored by the Basic Energy Science (BES) Program, DOE Office of Science.

Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such an identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose. This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).