# Exploring interfacial magnetism in all-spinel Fe3O4/MgCr2O4/Fe3O4 epitaxial heterostructures

Francesco Offi, Francesco Borgatti, Pasquale Orgiani, Vincent Polewczyk, Sandeep Kumar Chaluvadi, Shyni Punathum Chalil, Aleksandr Petrov, Federico Motti, Gian Marco Pierantozzi, Giancarlo Panaccione, et al.

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Francesco Offi, Francesco Borgatti, Pasquale Orgiani, Vincent Polewczyk, Sandeep Kumar Chaluvadi, et al.. Exploring interfacial magnetism in all-spinel Fe3O4/MgCr2O4/Fe3O4 epitaxial heterostructures. Nanoscale, In press, 10.1039/D5NR00971E. [hal-05106200](https://hal.science/hal-05106200v1)

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BORGATTI, P. Orgiani, V. Polewczyk, S. K. Chaluvadi, S. P. Chalil, A. Petrov, F. Motti, G. M. Pierantozzi, G.
Panaccione, B. Rutkowski, P. Mengucci, G. Barucca, D. Biswas, T. Lee, E. Marchetti, A. Martinelli, D. Peddis
and G. Varvaro, *Nanoscale*, 2025, DOI: 10.1039/D5NR00971E.

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Varvaro, Gaspare; Consiglio Nazionale delle Ricerche, Institute of Structure of Matter, nM2-Lab

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# Exploring Interfacial Magnetism in All-Spinel Fe₃O₄/MgCr₂O₄/Fe₃O₄ Epitaxial Heterostructures†

Francesco Offi,ª,ᵇ Francesco Borgatti,ᶜ,ᵈ Pasquale Orgiani,ᵇ Vincent Polewczyk,ᵇ,∥ Sandeep Kumar Chaluvadi,ᵇ Shyni Punathum Chalil,ᵇ Alexander Petrov,ᵇ Federico Motti,ᵇ Gian Marco Pierantozzi,ᵇ Giancarlo Panaccione,ᵇ Bogdan Rutkowski,ᵈ Paolo Mengucci,ᵉ Gianni Barucca,ᵉ Deepnarayan Biswas,ᵉ Tien-Lin Lee,ᵉ Emiliano Marchetti,ª,g Alberto Martinelli,ʰ Davide Peddis,⁵,i and Gaspare Varvaro⁶

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Epitaxial heterostructures integrating thin Fe₃O₄ films hold great potential for spintronics, magnetonics, and multifunctional device development. In this work, the morpho-structural and magnetic properties of all-spinel Fe₃O₄/MgCr₂O₄/Fe₃O₄ trilayers grown on a MgCr₂O₄ buffer layer, exhibiting very close lattice matching, were investigated by using both surface and bulk sensitive techniques. The close lattice match between Fe₃O₄ and MgCr₂O₄ enables the growth of epitaxial heterostructures with magnetically decoupled Fe₃O₄ layers for spacer thicknesses ≥ 1.6 nm, while reducing the formation of antiphase boundaries. Despite localized interphase diffusion, which leads to the formation of a mixed Cr/Fe spinel oxide with magnetically polarized Cr ions at the Fe₃O₄/MgCr₂O₄ interfaces, the overall magnetic properties remain largely consistent with those of the individual Fe₃O₄ layers. This study sheds light on the magnetic interactions within Fe₃O₄ layers mediated by a MgCr₂O₄ spacer, and demonstrates the feasibility of the approach in preserving the properties of thin Fe₃O₄ films, in complex heterostructures, thus offering a promising pathway for designing advanced all-spinel oxide devices.

## 1 Introduction

Ferroic transition metal oxides (TMOs) have attracted a great deal of attention for both fundamental studies and technological appli-

cations.¹ The variable oxidation states of transition metals allow the formation of several compounds, exhibiting a wide range of physical properties resulting from the strong coupling between charge, spin, orbital and lattice symmetry.²,³ Novel functional materials, in form of thin films, with tailored chemical and physical properties can be designed by changing the nature of each component, their relative thickness, or by tuning the interface interactions. Magnetic spinel oxides (MFe₂O₄) containing 3d metals (M = Fe, Co, Ni, Mn, ...) represent one of the most interesting classes of TMOs due to their excellent chemical stability and rich crystal chemistry, allowing for an excellent fine-tuning of the magnetic properties.⁴,⁵

Among family members, magnetite (Fe₃O₄) is of particular interest due to its unique magnetic and electrical properties.⁶ Fe₃O₄ is a conductive and biocompatible material, showing ferrimagnetic characteristics, with a high Curie temperature (858 K), a theoretically predicted half-metal behavior and an experimentally observed spin polarization of almost 100% at the Fermi level.⁷ These remarkable properties make Fe₃O₄ highly promising for various fields, including biomedicine,⁸ spintronics,⁹ magnetoeionics,¹⁰ soft robotics,¹¹ and multi-physics devices.¹² Owing to its

Nanoscale Accepted Manuscript

<footnote>ª Dipartimento di Scienze, Università Roma Tre, I-00146, Rome, Italy.</footnote>

<footnote>ᵇ CNR - Istituto Officina dei Materiali (IOM), Area Science Park, I-34149 Trieste, Italy.</footnote>

<footnote>ᶜ Istituto per lo Studio dei Materiali Nanostrutturati (ISMN), Consiglio Nazionale delle Ricerche (CNR), I-40129 Bologna, Italy.</footnote>

<footnote>ᵈ AGH University of Krakow, Faculty of Metals Engineering and Industrial Computer Science, Kraków 30-059, Poland.</footnote>

<footnote>ᵉ Department SIMAU, University Politecnica delle Marche, Via Brecce Bianche, I-60131, Ancona, Italy & UdR INSTM Ancona, Italy.</footnote>

<footnote>f Diamond Light Source Ltd., Diamond House, Harwell Science and Innovation Campus, Didcot OX11 0DE, United Kingdom.</footnote>

<footnote>g National Research Council, Institute of Structure of Matter, nM2-Lab, Research Area Roma 1, Monterotondo Scalo (Roma), I-00015, Italy.</footnote>

<footnote>h CNR-SPIN, I-16152 Genova, Italy.</footnote>

<footnote>i Università degli Studi di Genova, Dipartimento di Chimica e Chimica Industriale & INSTM RU, nM2-Lab, I-16146 Genova, Italy.</footnote>

<footnote>† Supplementary Information available:</footnote>

<footnote>‡ Corresponding author. E-mail: francesco.borgatti@cnr.it</footnote>

<footnote>¶ Present address: Université Paris-Saclay, UVSQ, CNRS, GEMaC, 78000 Versailles, France.</footnote>
peculiar properties, Fe₃O₄ films have been widely investigated as key component of different thin film heterostructures including hard/soft all-oxide composites, hybrid and all-oxide spintronic structures, and multilayers/superlattices consisting of magnetite thin films separated by a thin spacer layer.¹³⁻²⁴ Previous studies on Fe₃O₄-based multilayers/superlattices have demonstrated the richness of interface-induced phenomena occurring in such structures as a function of the spacer, including thickness-dependent antiferromagnetic/ferrimagnetic interface coupling, stabilization of thin magnetite layers, modulation of saturation magnetization and magnetic anisotropy.¹⁷⁻²³ The intricate interplay at the interface drives the magnetic characteristics of those structures, underscoring the significance of interface conditions in shaping the overall magnetic behaviour.¹⁹,²²,²⁵ To date, only a few spacers, such as MgO, MgFe₂O₄, Mn₃O₄, PtSe₂, and TiN, have been explored, implying that there is potential to observe additional phenomena using alternative materials with selected characteristics.

In this work, we have investigated the interface structure of Fe₃O₄-based trilayers consisting of thin ferrimagnetic Fe₃O₄ layers (7 nm) separated by a ultra-thin MgCr₂O₄ spacer with thicknesses of 0.6 nm, 1.6 nm and 2.4 nm grown on an MgAl₂O₄ (100) substrate covered with a thick MgCr₂O₄ buffer layer. MgCr₂O₄ is a spinel oxide exhibiting a favorable lattice parameter match with Fe₃O₄ (aFe₃O₄ = 8.394 Å, aMgCr₂O₄ = 8.333 Å, where aₓ is the lattice constant of the X compound).²⁶ Bulk MgCr₂O₄ is a semiconductive antiferromagnet that is paramagnetic above 12.5 K,²⁷,²⁸ which is expected to exhibit insulating behavior at low thicknesses, similar to other TMOs.²⁹ The same crystal symmetry and the comparable lattice constant are expected to result in epitaxial Fe₃O₄/MgCr₂O₄ heterostructures with coherently grown interfaces. Our results demonstrate that epitaxial structures indeed form, with the two Fe₃O₄ layers behaving independently for spacer thickness ≥ 1.6 nm. The heterostructure shows reduced coercivity compared to thick Fe₃O₄ films directly deposited on MgO (100) substrates, an effect attributed to a reduction of the antiphase boundary due to the excellent lattice match between Fe₃O₄ and the MgCr₂O₄ buffer layer. Although localized intermixing at the Fe₃O₄/MgCr₂O₄ interfaces induces magnetic polarization in Cr ions, this has minimal influence on the overall magnetic behaviour, which remains primarily governed by the individual Fe₃O₄ layers. These insights deepen our understanding of the magnetic interaction among spinel oxide layers, facilitating the development of functional full-oxide devices.

## 2 Experimental

Fe₃O₄/MgCr₂O₄/Fe₃O₄ thin film heterostructures were deposited on an MgCr₂O₄ buffer layer grown on single-crystal (100)-oriented MgAl₂O₄ spinel substrates by Pulsed Laser Deposition (PLD) at the NFFA laboratories, located within the Elettra synchrotron radiation facility in Trieste, Italy.³⁰ While ultraviolet excimer lasers (λ = 248 nm) are conventionally employed for the deposition of complex oxide heterostructures³¹, this study used a first harmonic Nd:YAG solid-state laser (1064 nm), which has recently demonstrated efficacy in producing high quality oxide films while offering a simpler experimental setup.³²⁻³⁵ The deposition parameters were optimized for the individual Fe₃O₄ and

MgCr₂O₄ layers, with the substrate temperature set to 500°C. The growth was performed at laser repetition rates of 0.5 Hz and 1 Hz for Fe₃O₄ and MgCr₂O₄, respectively. Calibration of the growth rates via X-ray reflectivity yielded values of 0.02 nm and 0.008 nm per laser pulse, ensuring precise control over the layer thickness during deposition (see Supplementary Information for growth details). While a commercial target was used for Fe₃O₄, an home-made one was employed for MgCr₂O₄ (see Supplementary Information for fabrication details). To minimize the lattice mismatch between Fe₃O₄ and the substrate [(aFe₃O₄ - aMgAl₂O₄)/aMgAl₂O₄ ~ 3.8%) and promote the formation of epitaxial thin films, the MgAl₂O₄ substrate was coated with a MgCr₂O₄ buffer layer with a nominal thickness of 30 nm, high enough to relax the strain induced by the substrate and reach the lattice parameter of bulk MgCr₂O₄, which closely matches that of the Fe₃O₄ layer, [(aFe₃O₄-aMgCr₂O₄)/aMgCr₂O₄ ~ 0.7%). The critical thickness t_c of the MgCr₂O₄ on the MgAl₂O₄ substrate, above which the system exhibits strain relaxation, was estimated employing the Fischer, Kuhne, and Richards (FKR) model,³⁶ obtaining a value of about t_c = 17 nm (details in the Supplementary Information). On top of this buffer layer, trilayers consisting of two thin Fe₃O₄ films, each with a thickness of 7 nm, separated by an MgCr₂O₄ spacer with varying thicknesses (0.6 nm, 1.6 nm and 2.4 nm) were grown. For comparison, a thick Fe₃O₄ film with a thickness of 60 nm on MgO (100) single crystal substrate, as well as a single 7 nm thick Fe₃O₄ film deposited on MgAl₂O₄ (100), with and without an MgCr₂O₄ buffer layer, were grown under identical experimental conditions.

A comprehensive set of advanced measurements was conducted at room temperature to correlate the morpho-structural and magnetic properties of the samples. Magneto optical Kerr effect (MOKE) measurements,³⁷ with laser wavelength of 405 nm, and X-ray absorption spectroscopy (XAS) with in remanence (±0.05 T) X-ray magnetic circular dichroism (XMCD) investigation at the Cr and Fe L₂,₃ absorption thresholds were executed under ultra-high vacuum conditions at the APE-HE beamline.³⁸ These latter measurements were performed in total electron yield (TEY) mode with the X-ray beam incident at 45° and an energy resolution of about 0.1 eV. In addition, HArD X-ray PhotoEmission Spectroscopy (HAXPES) measurements were conducted at beamline I09 of the Diamond Light Source (UK),³⁹ on samples transported in protective atmosphere and introduced in the experimental chamber without air exposition. Photon energies of hν = 1.78, 4.05, 8.08 keV (in all cases incidence angle was 20° from the sample surface) were set to obtain information at different depths with a total energy resolution at the different photon energies of 0.39, 0.25, and 0.27 meV, respectively. Structural characterization involved the use of ex-situ X-ray reflectivity and high resolution scanning transmission electron microscope (HR-STEM). STEM observations on thin-film cross-sections (see Supplementary Information for details about sample preparation) were performed using a probe Cs-corrected FEI Titan³ G2 60-300 STEM equipped with ChemiSTEM technology (X-FEG field emission gun and Super-X EDX detector system) developed at FEI.⁴⁰ The latter allows for the chemical composition analysis of the layers down to the nanoscale with the energy-dispersive X-
ray (EDX) microanalysis. Integral magnetic measurements were performed at room temperature using a commercial MicroSense Model 10 vibrating sample magnetometer (VSM) with the magnetic field applied in the film plane along the (100) direction of the MgAl₂O₄ substrate. Semi-empirical calculations of the XAS and XMCD spectra were performed within the framework of the atomic multiplet and ligand field theory using the QUANTY program.⁴¹ Details of the theoretical model can be found in the book of de Groot and Kotani.⁴²

# 3 Results and discussion

## 3.1 Structural characterization

Figures 1(a) and 1(b) present the crystallographic structures of Fe₃O₄ and MgCr₂O₄, highlighting the ion site occupancy, and the schematic structure of the multilayer, respectively. Figure 1(c,d) show the high-resolution (HR) high-angle annular dark field (HAADF) STEM images of samples with a MgCr₂O₄ spacer thickness of 0.6 and 2.4 nm, respectively. The high degree of epitaxial matching is evident in all the investigated samples, hence highlighting the structural quality of the whole heterostructure (see also the noise-filtered images reported in Figures SI1 and SI5 of the Supplementary Information). The samples reveal the expected cubic structure (Figures SI2 and SI6) with the (001) planes parallel to the substrate surface, and pictures (c) and (d) are taken in [100] and [110] zone-axis orientation.

Close inspection of the STEM image in panel (d) points out the presence of anti-phase boundaries (APBs) in the MgCr₂O₄ buffer layer, associated with displacement vectors of $a/4 < 110>$.⁴³,⁴⁴ In the white squared inset, the contrast variation in the periodic distribution of atoms in the MgCr₂O₄ buffer layer along the direction indicated by the dashed line is evident, and it is assigned to the presence of an $a/4[1\bar{1}0]$ APB producing the corresponding shift of the $(\bar{1}11)$ lattice planes. Although generally expected in all samples, APBs are not visible in panel (c) because the sample is in [100] zone axis orientation and, as can be deduced from the inset of Figure SI5(b): a shift of $a/4[011]$ of the lattice does not give rise to a new atomic distribution that can be distinguished by the Z (atomic number)-contrast of the HAADF-STEM technique. The presence of APBs in the MgCr₂O₄ buffer layer is due to the formation of partial dislocations that relax the strain induced by the mismatch with the MgAl₂O₄ substrate.³⁶ The mismatch evolution across the whole heterostructures was investigated by performing fast Fourier transforms (FFTs) in different regions of the images [insets in Figure 1(c) and 1(d)] and calculating the $d(040)$ and $d(220)$ interplanar distances, which are parallel to the substrate, reported in Table 1 [the values tabulated at the International Centre for Diffraction Data (ICDD) for MgAl₂O₄ (ICDD card n° 21-1152) are used to calibrate the FFT images]. The values listed in Table 1 show that the MgCr₂O₄ buffer layer is relaxed in proximity to the bottom Fe₃O₄ layer because its measured interplanar distances agree with the tabulated values for the bulk material (ICDD card no. 10-0351) within experimental errors. Similarly, the interplanar distances of the Fe₃O₄ layers are consistent with the bulk values (ICDD card n° 19-0629), indicating a complete relaxation of the magnetic films. Despite the perfect lattice match-

ing at the interface between the MgCr₂O₄ buffer layer and the Fe₃O₄ film, HR-STEM analysis reveals the presence of APBs in the Fe₃O₄/MgCr₂O₄/Fe₃O₄ trilayers (see Figure SI3). In this case, the origin of the APBs cannot be attributed to the mismatch between the cell parameters of the MgCr₂O₄ buffer layer and the Fe₃O₄, since they show relaxed values, and therefore a comparable lattice parameter, but more likely due to the propagation of the APBs defects from the MgCr₂O₄ to the Fe₃O₄/MgCr₂O₄/Fe₃O₄ trilayers. Noticeably, STEM-EDX measurements demonstrate that the elemental distribution inside the epitaxial heterostructures, shown in Figure 1(c,d) and Figures SI4 - SI7, is largely consistent with the actual thickness of each layer. These measurements are consistent with the results from the X-ray reflectivity analysis (see Supplementary Information, Figure S8), which indicate the presence of relatively flat interfaces with a root mean square roughness of 0.2–0.3 nm. The elemental intensity profiles along the vertical direction are shown in panels (e,f) of Figure 1, starting from the sample surface (left side) towards the MgAl₂O₄ substrate (right side). It is interesting to observe that Fe and Cr appear to diffuse into each other’s layer at the top of the sample, and that the Fe signal is visible in the whole MgCr₂O₄ interlayer. Moreover, the spectral comparison clearly indicates that the Fe intensity significantly decreases as the distance from the interfaces increases for the 2.4 nm thick interlayer, thus suggesting a greater ability of the spacer to separate the magnetic phases as its thickness increases. Considering the presence of interdiffusion, the formation of regions with intermediate stoichiometries cannot be excluded.

## 3.2 Chemical states

The chemical states of Fe and Cr ions were investigated by core-level HAXPES. This information is particularly relevant to recognize the presence of secondary phases formed during the growth, and/or at the boundaries among the layers that might also involve significant changes of the chemical states for the Fe and Cr ions. Figure 2 shows the Fe $2p$ and Cr $2p$ core level spectra of the thin film heterostructure with a MgCr₂O₄ spacer thickness of 0.6 nm. The spectra acquired for samples with a thicker MgCr₂O₄ spacer provide similar results. With the incident photon energy varying from 1.78 keV to 8 keV, the information depth ranges from about 6 nm ($h\bar{v}$ = 1.78 keV) to 25 nm ($h\bar{v}$ = 8 keV), as sketched in the inset of panel (a), hence the spectra refer to different regions of the heterostructure. Thus, the Fe $2p$ spectrum collected at 1.78 keV is only related to the upper Fe₃O₄ layer, consistently with the absence of Cr $2s$ and any spectral contribution of Cr in the survey spectrum (not shown here), suggesting that Cr diffusion in the top magnetite layer is mainly localized at the interface only. At higher photon energy, the Fe $2p$ spectra encompass the entire trilayer structure and also the Cr $2s$ and Cr $2p$ peaks [Figure 2(b)] are observed. Additionally, the Cr spectra for $h\bar{v}$ = 4 keV are indicative only of the MgCr₂O₄ interlayer, while those for $h\bar{v}$ = 8 keV contain a large bulk contribution of the underlying MgCr₂O₄ buffer layer. The latter thus provides a useful reference to distinguish changes in the electronic states of Cr ions in the thin MgCr₂O₄ interlayer.

The Fe $2p$ spectra shown in Figure 2 exhibit typical characteris-
<figure><img src="image_5.png" /><figcaption>Fig. 1 (a) inverse and normal spinel structure of Fe<sub>3</sub>O<sub>4</sub> and MgCr<sub>2</sub>O<sub>4</sub>: in Fe<sub>3</sub>O<sub>4</sub> quarter of the tetrahedral positions of the lattice are occupied by Fe<sup>2+</sup> ions while in half of the octahedral ones sit Fe<sup>2+</sup> and Fe<sup>3+</sup> cations; in MgCr<sub>2</sub>O<sub>4</sub>, Mg<sup>2+</sup> occupy the tetrahedral positions and Cr<sup>3+</sup> cations the octahedral ones. (b) Sketch of the Fe<sub>3</sub>O<sub>4</sub>/MgCr<sub>2</sub>O<sub>4</sub>/Fe<sub>3</sub>O<sub>4</sub> heterostructure deposited on top of a thick MgCr<sub>2</sub>O<sub>4</sub> buffer layer grown on the MgAl<sub>2</sub>O<sub>4</sub>(001) substrate. (c,d) High-resolution HAADF-STEM image for heterostructures with a MgCr<sub>2</sub>O<sub>4</sub> spacer of 0.6 nm (c) and 2.4 nm (d). Black dashed lines indicate the different compound regions. The samples in panels (c) and (d) were [100] and [110] zone-axis oriented, respectively. Insets display FFTs performed in the corresponding regions of the heterostructures. The resulting interplanar distances are reported in Table 1. (e,f) Elemental distribution among the layers as achieved by STEM-EDX measurements. The intensity is not scaled to the formula unit composition. To better elucidate the details of STEM images, further information such as EDX elemental maps for Al, Mg, Fe and Cr and noise-filtered HR-STEM images are reported in Figures S1-S17 of the Supplementary Information.</figcaption></figure>

tics of the Fe₃O₄ phase, as reported in previous studies.⁴⁵,⁴⁶ The consistency of the spectra across a wide range of probing depth highlights the high quality of both magnetite layers and suggest the absence of significant deviations from the nominal stoichiometry. This conclusion is further supported by the fitting analysis of the Fe 2p₃/₂ peaks performed following the model described by Grosvenor et al., where the contribution of Fe 2+ (Fe 3+) ion is identified at lower (higher) binding energy and each of the two is made up of several components deriving from multiplet splitting, surface components and satellites.⁴⁷ This analysis successfully disentangles the spectral terms contributions from Fe²⁺ and Fe³⁺, yielding a Fe³+/Fe²⁺ intensity ratio of ~1.7, in good agreement with the expected ideal concentration ratio of 2:1. Note also that, in the spectral region between the two spin-orbit-splitted edges, the satellite structure that is prominent in the photoemission spectra of α-Fe₂O₃ (hematite) and γ-Fe₂O₃ (maghemite) is not visible in the present case.⁴⁸ Such satellite structure is due to charge transfer screening and it is visible, at somehow different binding energies, for iron oxides purely Fe²⁺ (such as FeO) or Fe³⁺ (such as Fe₂O₃), its intensity smearing out when both ionic components are present (such as in Fe₃O₄).⁴⁹ This implies that only magnetite is present in the investigated heterostructures and

no other iron oxide phases are formed. This is particularly relevant for the Fe 2p spectrum for $h\nu = 1.78$ keV, being the most sensitive to the surface.

The Cr 2s and Cr 2p spectra shown in panel (a) and (b), respectively, provide further confirmation of these results. The similarity of the spectra, despite the substantial differences of the probing depth, indicates that the chemical state of the Cr ions of the spacer closely resembles that of the thick MgCr₂O₄ buffer layer, suggesting the absence of secondary phases related to different chemical states, e.g. as Cr²⁺ in CrO₂. The multiplet splitting features resulting from the fitting analysis of the Cr 2p₃/₂ spectrum, with the energy splitting $\Delta_{AB} = 1.04 - 1.09$ eV, resemble closely those of the α-Cr₂O₃ or CrFe₂O₄ phase, where the Cr³⁺ ions exclusively occupy octahedral lattice sites.⁵⁰,⁵¹ This strongly suggests that Cr ions in our sample predominantly reside in the octahedral sites, as expected for the normal spinel structure of MgCr₂O₄. On the other hand, the observed spectral features are also compatible with the formation of a Cr/Fe mixed spinel oxide as long as this phase maintains the chemical state and site symmetry of the Fe and Cr ions. The formation of such phase at both the Fe₃O₄/MgCr₂O₄ interfaces cannot be ruled out, and indeed it is the most plausible hypothesis to explain the observed magnetic
<table><caption>Table 1 Interplanar distances obtained from FFTs of images taken from various regions of the heterostructure and for different MgCr₂O₄ interlayer thicknesses, as shown in Figure 1(c) and 1(d). The top and bottom Fe₃O₄ layers were analyzed, yielding identical interplanar distances in both cases.</caption><thead><tr><th></th><th>Bulk material<br>d(040) (nm)</th><th>Bulk material<br>d(220) (nm)</th><th>MgCr<sub>2</sub>O<sub>4</sub> 0.6 nm<br>d(040) (nm)</th><th>MgCr<sub>2</sub>O<sub>4</sub> 2.4 nm<br>d(220) (nm)</th></tr></thead><tbody><tr><td>Fe<sub>3</sub>O<sub>4</sub></td><td>0.2099</td><td>0.2967</td><td>0.210±0.002</td><td>0.296±0.002</td></tr><tr><td>Fe<sub>3</sub>O<sub>4</sub></td><td>0.2099</td><td>0.2967</td><td>0.210±0.002</td><td>0.296±0.002</td></tr><tr><td>MgCr<sub>2</sub>O<sub>4</sub></td><td>0.2083</td><td>0.2945</td><td>0.206±0.002</td><td>0.293±0.002</td></tr><tr><td>MgAl<sub>2</sub>O<sub>4</sub></td><td>0.2020</td><td>0.2858</td><td></td><td></td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Fig. 2 Fe 2p (a) and Cr 2p (b) core level spectra for the Fe₃O₄(7 nm)/MgCr₂O₄(0.6 nm)/Fe₃O₄(7 nm) trilayer. Spectra are normalized to the maximum intensity. The Fe 2p spectra also shows Cr 2s peak closely located to the Fe 2p₃/₂ one. The information depth of the spectra, sketched in the inset of panel (a), ranges from about 6 nm ($h\nu = 1.78$ keV) to 25 nm ($h\nu = 8$ keV).</figcaption></figure>

measurements, as described in the next sections.

### 3.3 Magnetic investigation

The overall magnetic behaviour of the spinel oxide heterostructures is elucidated by a comparative study of VSM and MOKE measurements, shown in Figure 3 and Fig. SI9. Field-dependent magnetization loops of thin film heterostructures for different

<figure><img src="image_7.png" /><figcaption>Fig. 3 (a,b) In-plane VSM (left scale) and longitudinal MOKE (right scale) field-dependent magnetization loops, M(H), at 300 K of trilayer heterostructures with an MgCr₂O₄ spacer thickness of (a) 0.6 nm and (b) 2.4 nm; (c) M(H) loop of a 7 nm thick Fe₃O₄ film reference film grown on an MgCr₂O₄ buffer layer.</figcaption></figure>

MgCr₂O₄ spacer thicknesses are compared to that of a 7 nm thick Fe₃O₄ film deposited on the MgCr₂O₄ buffer layer to gain insights into the factors influencing the magnetic properties of the spinel oxide heterostructure. If we consider the penetration depth of the laser ($\lambda = 400$ nm) of about 20 nm,⁵² the magnetic information obtained by MOKE primarily relates to the thin film heterostructure and the MgCr₂O₄ buffer layer, while VSM provides the magnetization evolution of the entire sample, potentially including any magnetic contributions from the substrate. Due to the presence of ferro(i)magnetic impurities within the substrate, VSM measurements were corrected to account for both the dia-
magnetism of the substrate and the ferromagnetic contribution of the contaminants (Figure SI10 in the Supplementary Information). However, precise quantification of contamination levels in each sample proved challenging, impacting the correction's precision. This issue may lead to underestimations or overestimations of the magnetization value based on the correction method (as detailed in the Supplementary Information and shown in Figure SI10), especially in the high-field region, where the approach of magnetization to saturation can potentially be influenced by the presence of APBs.⁵³ Therefore, a reliable determination of the saturation magnetization is unfeasible. On the other hand, the correction had a minimal effect in the low-field region, as detailed in the Supplementary Information. The agreement of the corrected VSM loops with the MOKE loops, collected in the ± 0.1 T field region, supports the reliability of the magnetic measurements within this specific range, offering a dependable benchmark for studying and comparing the samples' magnetic properties. Both the single Fe₃O₄ layer and the trilayers exhibit almost square loops, indicating a magnetically homogeneous film with a strong level of magnetic ordering.⁵⁴ Furthermore, the measured hysteresis loops reveal relatively low coercive field, with μ₀H_c = 7.0(5) mT for the single Fe₃O₄ layer, and μ₀H_c = 12.5(5) mT, 6.5(3) mT and 5.0(3) mT for the trilayers containing MgCr₂O₄ spacers of 0.6 nm, 1.6 nm and a 2.4 nm thickness, respectively. These values are significantly lower than those observed for Fe₃O₄ thin films deposited directly on MgAl₂O₄(100) substrates without an MgCr₂O₄ buffer layer (see Figure SI11 in the Supplementary Information), thus suggesting that adding an MgCr₂O₄ buffer layer can reduce the density of APBs, typically resulting in increased coercivity through pinning effects.⁵⁵,⁵⁶ Additionally, the similarity in coercivity between the trilayer with a 1.6 nm and 2.4 nm thick MgCr₂O₄ spacer and the single Fe₃O₄ film suggests that the two magnetite films are effectively separated, behaving almost as individual entities. The rise in coercivity in the trilayer with a 0.6 nm thick MgCr₂O₄ spacer may be linked to the films' quasi-continuous nature, as greater thicknesses may correspond to higher coercivity, as observed in some studies focusing on similar low thickness regions.⁵³,⁵⁷,⁵⁸ This scenario could be somehow more complex if we consider the formation of a mixed Cr/Fe spinel oxide at Fe₃O₄/MgCr₂O₄ interfaces, contributing to the overall magnetic configuration, as reported by Vasconcelos et al. for the corresponding thin films.⁵⁹ Thus, besides the occurrence of APBs, the presence of mixed interface phases could play a role for driving the magnetic properties of the entire heterostructure.

## 3.4 XAS and surface magnetic properties

Figure 4 summarizes the XAS/XMCD results obtained for samples with MgCr₂O₄ spacer thickness ranging from 0.6 nm to 2.4 nm. The quantitative estimation of the XAS/XMCD depth sensitivity in total yield mode still remains not completely defined. While it has been clarified that the sample depth probed by these measurements must be less than 20 nm⁶⁰, XAS measurements of Fe L₂,₃ absorption thresholds from Fe₃O₄ are reported with mean probing depth values from about 1 to 5 nm⁶¹,⁶², which demonstrates the

high uncertainty in this value and the relatively high surface sensitivity of the technique. Therefore, we can safely assume that the spectra of Figure 4 probe the upper part of the trilayer structure, i.e. the top Fe₃O₄ layer and the MgCr₂O₄ spacer, in particular excluding any contribution from the interface at the MgCr₂O₄ buffer layer. The x-ray absorption spectra of the Fe and Cr L₂,₃ absorption thresholds for the sample with MgCr₂O₄ spacer thickness 0.6 nm, obtained by averaging over the dichroic curves, are shown in panels (a,b). Similar spectra (not shown) are obtained for the other MgCr₂O₄ spacer thicknesses. The Fe L₂,₃ spectrum is consistent with most of those reported in literature for magnetite, hence confirming the good quality of these layers.⁶³,⁶⁴ On the other hand, the Cr L₂,₃ spectrum is very similar to that of compounds hosting Cr³⁺ (3d³) ions located in lattice sites with local octahedral symmetry O_h, such as in Cr₂O₃,⁵⁹,⁶⁵⁻⁶⁷ thus reinforcing the hypothesis to having obtained the correct MgCr₂O₄ crystallographic structure, where indeed the chromium ions solely occupy the octahedral sites. Thus, the analysis of the Fe L₂,₃ and Cr L₂,₃ absorption spectra suggest the heterostructure does not host spurious phases containing different oxidation states, in agreement with the HAXPES results. In particular, the absence of significant contribution by Cr²⁺ ions rule out the presence of room-temperature ferromagnetic CrO₂. In order to put these considerations on a firmer ground, we performed theoretical calculations, shown as red lines superimposed to the experimental spectra of Figure 4(a) and Figure 4(b), confirming the above interpretation: The Cr L₂,₃ absorption spectrum was calculated for Cr³⁺ valence state in octahedral local symmetry, consistently with the position of Cr ions in the MgCr₂O₄ lattice, while the calculation for the Fe L₂,₃ absorption spectrum accurately incorporates the contribution of all Fe cations, i.e. Fe²⁺ in octahedral symmetry (O_h), Fe³⁺ in tetrahedral symmetry (T_d) and Fe³⁺ in octahedral symmetry (O_h). The calculations were performed for an infinite material and then adjusted to match the experimental intensity. In particular, for the iron case, the theoretical curve is obtained from the sum of the three different Fe contributions, weighted in order to obtain the best representation of the experimental data. The corresponding theoretical XMCD curves for each ion species are reported in panels (e,f).⁶³,⁶⁴,⁶⁸,⁶⁹

Although the shape and strength of the Fe XMCD is largely consistent with previous results about thin films of magnetite,⁷⁰ the occurrence of a sizeable XMCD for Cr in MgCr₂O₄ is unexpected, as MgCr₂O₄ is an antiferromagnetic semiconductor with a Néel temperature of about 13 K, and paramagnetic at room temperature. Accordingly, we indeed find out that the XMCD signal at the Cr L₂,₃ absorption edges was vanishing in a single MgCr₂O₄ film (not shown). The XMCD curves of Cr and Fe ions in panel (c) and (d), respectively, show consistent lineshape but varying intensity for increasing spacer thickness. In particular, the trilayers with MgCr₂O₄ spacers of 1.6 nm and 2.4 nm show nearly identical XMCD spectral features and comparable amplitude, indicating that both configurations result in effective magnetic decoupling of the Fe₃O₄ layers. Note that the calculation shown in Figure 4(e), indicating a sizable XMCD for Cr³⁺ ion, do not take into account the whole MgCr₂O₄ structure. The sign of the XMCD curves for Fe and Cr indicates that the Cr magnetic moments are oriented

Nanoscale Accepted Manuscript
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 4 XAS/XMCD measurements at the Fe and Cr L$_{2,3}$ absorption thresholds. (a,b) experimental (black dotted lines) and calculated (red lines) x-ray absorption curves. All spectra were collected at room temperature with the samples in the remanent state. (c,d) XMCD curves for different thickness of the MgCr$_{2}$O$_{4}$ spacer. The XMCD curves are normalized to the maximum average intensity of the L$_{3}$ absorption threshold in the respective Fe and Cr spectra. The XMCD curves are well reproduced by calculations (red lines) reported in panels (e,f). Calculated XMCD curves used to reproduce the experimental results. Details of calculations are reported in the text.</figcaption></figure>

as those of the Fe$^{2+}$/3+ ions in the octahedral sites of the magnetite, thus ruling out the presence of Cr ions in the tetrahedral sites. This condition resembles the ferromagnetic state of Cr for the iron chromite CrFe$_{2}$O$_{4}$,⁶⁵ where the Cr$^{3+}$ ions only occupy lattice sites with $O_h$ symmetry. Furthermore, the XMCD curves of Cr are fully consistent with the XMCD calculation shown in panel (e) based on the same configurational parameters of the absorption threshold, except for a scale factor adopted to fit the change of the experimental XMCD amplitude. This indicates the formation of mixed phases at the Fe$_{3}$O$_{4}$/MgCr$_{2}$O$_{4}$ boundaries in which the replacement of Fe by Cr in the lattice promotes the magnetic ordering of the Cr magnetic moments.

To investigate this replacement process in the Fe$_{3}$O$_{4}$ lattice, we have analysed in detail the lineshape of the Fe XMCD curves in the L$_{3}$ energy region. In Figure 5, the XMCD curves for the samples with the thinner (0.6 nm) and larger (2.4 nm) MgCr$_{2}$O$_{4}$ spacer thickness, and for a 60 nm thick film of Fe$_{3}$O$_{4}$ used as reference for the bulk, are normalized to the maximum XMCD. This procedure highlights the reduction of XMCD in the energy region associated to the Fe$^{2+}$ contribution upon increasing MgCr$_{2}$O$_{4}$ spacer thickness. We have evaluated the relative concentration of the Fe$^{2+}$(O$_{h}$), Fe$^{3+}$(T$_{d}$), and Fe$^{3+}$(O$_{h}$) components in the Fe XMCD curves by fitting the L$_{3}$ energy region with the three dichroic contributions shown in Figure 4(f). This ap-
<figure><img src="image_10.png" /><figcaption>Fig. 5 Experimental and theoretical XMCD curves at the Fe L$_{3}$ absorption threshold for different MgCr$_{2}$O$_{4}$ thickness and the reference Fe$_{3}$O$_{4}$ thick layer. The XMCD curves are normalized to the maximum to emphasize the change in the low energy region. The theoretical XMCD curves were obtained by fitting the contribution of the different Fe ions in the Fe$_{3}$O$_{4}$ lattice.</figcaption></figure>

proach proved fruitful information in other cases involving Fe$_{3}$O$_{4}$ or Fe$_{2}$O$_{3}$.⁶⁴ As shown in Figure 5, the fitting results obtained by proper weighting of the three dichroic contributions confirm the evolution of the experimental curves, with the relative amount of Fe$^{2+}$(O$_{h}$):Fe$^{3+}$(T$_{d}$):Fe$^{3+}$(O$_{h}$) passing from 0.92:1:1 for the thinner MgCr$_{2}$O$_{4}$ spacer to 0.85:1:1 for the thicker one.

Such behavior is consistent with a scenario in which Fe$_{3}$O$_{4}$ with MgCr$_{2}$O$_{4}$ diffuse at their interface, forming a mixed region, as also evidenced by the EDX-STEM results, where Cr$^{3+}$ partially replaces Fe$^{2+}$ (in octahedral coordination), which could then be oxidized to Fe$^{3+}$.⁷¹ This leads to the formation of a mixed spinel oxide at the Fe$_{3}$O$_{4}$/MgCr$_{2}$O$_{4}$ interfaces, containing both iron and chromium ions. Compared to pure Fe$_{3}$O$_{4}$, this phase exhibits lower saturation magnetization and softer magnetic properties, in agreement with literature data on mixed Cr/Fe spinel oxides.⁵⁹ In this phase, Cr$^{3+}$ ions acquire a magnetic polarization, and the relative proportions of iron species in Fe$_{3}$O$_{4}$ are modified, consistent with the characteristics of mixed Cr/Fe spinel oxides. As a result, the enhanced XMCD signal observed in the thinner MgCr$_{2}$O$_{4}$ layer [~20%, as shown in Figure 4(c)] may be linked to the low chromium content at the interface. As the thickness of the MgCr$_{2}$O$_{4}$ layer increases, more Cr ions is available to diffuse thorough the interface, leading to the formation of a mixed Cr/Fe spinel phase with a higher chromium concentration compatible with a decrease in the Cr XMCD signal and in a decrease in the coercive field, as observed by Vasconcelos Borges Pinho et al.⁵⁹

It has to be noted that in a complex system such as magnetite, characterized by the interaction of different Fe valences, the exact balance between the various Fe ions is fundamental for establishing certain magnetic behaviours. For example, it is quite common that in Fe$_{3}$O$_{4}$ films an Fe(ochtahedral)-O termination is the most favourable,⁷² and in general it has been reported that the Fe$_{3}$O$_{4}$ surface is richer of Fe$^{3+}$ (O$_{h}$) than the bulk,⁷³,⁷⁴ leading to a decrease of the saturation magnetization. In particular, in the present case, the exact nature of the Fe$_{3}$O$_{4}$/MgCr$_{2}$O$_{4}$ interface could play a role in the magnetic behaviour of the investigated heterostructures. In this respect it might be helpful to quantify the magnetic moment of iron in Fe$_{3}$O$_{4}$ via the XMCD sum rules,⁷⁵ keeping in mind that the obtained values may have some uncertainties as due, for example, to the exact value of the number of 3d holes used (here 13.5 for all the samples) and the integration range for the magnetic moment estimation.⁶²,⁷⁶ As a consequence, the absolute values of the obtained magnetic moments might be questionable, while a relative comparison among the values obtained for the different samples remains reliable. The values of the spin (μ$_{spin}$), orbital (μ$_{orb}$) and total (μ) Fe magnetic moments in the three investigated trilayers, the 60 nm thick Fe$_{3}$O$_{4}$ grown on MgO(100) and the 7 nm thin Fe$_{3}$O$_{4}$ grown on MgCr$_{2}$O$_{4}$/MgAl$_{2}$O$_{4}$(100), are collected in Table 2.

<table><caption>Table 2 Fe magnetic moments obtained by XMCD sum rules.</caption><thead><tr><td>Sample</td><td>μ<sub>spin</sub> (μ<sub>B</sub>)</td><td>μ<sub>orb</sub> (μ<sub>B</sub>)</td><td>μ (μ<sub>B</sub>)</td></tr></thead><tbody><tr><td>60 nm Fe<sub>3</sub>O<sub>4</sub></td><td>1.88</td><td>1.10</td><td>1.98</td></tr><tr><td>7 nm Fe<sub>3</sub>O<sub>4</sub></td><td>1.11</td><td>0.30</td><td>1.41</td></tr><tr><td>0.6 nm MgCr<sub>2</sub>O<sub>4</sub></td><td>1.84</td><td>0.17</td><td>2.01</td></tr><tr><td>1.6 nm MgCr<sub>2</sub>O<sub>4</sub></td><td>1.51</td><td>0.07</td><td>1.58</td></tr><tr><td>2.4 nm MgCr<sub>2</sub>O<sub>4</sub></td><td>1.36</td><td>0.15</td><td>1.51</td></tr></tbody></table>

The iron magnetic moment of the trilayer with the thinnest MgCr$_{2}$O$_{4}$ spacer is basically equal to that of the 60 nm thick reference Fe$_{3}$O$_{4}$ sample (both values being however lower than the bulk value) and larger than that of a single 7 nm Fe$_{3}$O$_{4}$ film (corresponding XMCD spectra not shown in Figure 4 and reported in Supplementary Information Figure SI12). This observation suggests that the thinnest MgCr$_{2}$O$_{4}$ spacer does not fully decouple the two magnetite layers, causing the heterostructure to behave as a single Fe$_{3}$O$_{4}$ ferromagnetic film with an equivalent thickness of approximately 15 nm, as if the layers were in direct contact. In contrast, for MgCr$_{2}$O$_{4}$ spacers ≥ 1.6 nm, the magnetic moment in Fe$_{3}$O$_{4}$ decreases significantly to values similar to those of a single 7 nm Fe$_{3}$O$_{4}$ film. This indicates that the two layers behave almost independently, as they are effectively decoupled by the MgCr$_{2}$O$_{4}$ spacer with the Cr$_{x}$Fe$_{3-x}$O$_{4}$ phase being confined to the boundaries with Fe$_{3}$O$_{4}$, consistent with conclusions drawn from the magnetization curves. Indeed, the incorporation of Cr in Fe$_{3}$O$_{4}$, with the formation of the Cr$_{x}$Fe$_{3-x}$O$_{4}$, results in a reduction of the Fe magnetic moment with respect to pure magnetite,⁵⁹ thus if this alloy phase had not been limited to the interface alone, an even greater reduction in magnetic moments would have been observed.
## Conclusions

Epitaxial all-spinel Fe₃O₄/MgCr₂O₄/Fe₃O₄ heterostructures with variable spacer thicknesses were thoroughly investigated with a combination of chemical, morphological, structural, magnetic, and surface characterizations. For spacer thicknesses ≥ 1.6 nm, the two magnetite layers are effectively decoupled and behave as independent ferrimagnetic layers, thus demonstrating the feasibility of designing intricate all-oxide heterostructures that retain the intrinsic properties of individual thin Fe₃O₄ films. These samples exhibit relatively low coercivity, which is attributed to a reduced presence of antiphase boundaries due to the excellent lattice match between Fe₃O₄ and MgCr₂O₄ buffer layer. Limited cation interdiffusion occurs at the Fe₃O₄/MgCr₂O₄ interface, resulting in the formation of a mixed Cr/Fe spinel oxide phase localized at the interphase boundaries, which does not significantly affect the overall magnetic properties, remaining largely consistent with those of the individual Fe₃O₄ layers. This study provides insides into the magnetic interactions between Fe₃O₄ layers mediated by an MgCr₂O₄ spacer, demonstrating that thin Fe₃O₄ films can retain their intrinsic properties within complex heterostructures, paving the way for advanced all-spinel oxide devices with tailored functionalities.

## Author contributions

Francesco Offi: conceptualization, data curation, formal analysis, investigation, methodology, writing – original draft, writing – review & editing; Francesco Borgatti: data curation, formal analysis, investigation, methodology, writing – original draft, writing – review & editing; Pasquale Orgiani: investigation, methodology, writing – original draft; Vincent Polewczyk: data curation, formal analysis, writing – original draft; Sandeep Kumar Chaluvadi: data curation, investigation, writing – original draft; Shyni Punathum Chalil: data curation, investigation, writing – original draft; Alexander Petrov: data curation, formal analysis, investigation, methodology, writing – original draft; Federico Motti: data curation, investigation, writing – original draft; Gian Marco Pierantozzi: data curation, investigation, writing – original draft; Giancarlo Panaccione: funding acquisition, investigation, writing – original draft; Bogdan Rutkowski: data curation, formal analysis, funding acquisition, investigation, methodology, writing – original draft; Paolo Mengucci: writing – original draft; Gianni Barucca: investigation, methodology, writing – original draft; Deepnarayan Biswas: data curation, investigation, methodology, writing – original draft; Tien-Lin Lee: data curation, investigation, methodology, writing – original draft; Emiliano Marchetti: formal analysis, methodology, writing – original draft; Alberto Martinelli: methodology, writing – original draft; Davide Pedis: conceptualization, funding acquisition, investigation, writing – original draft; Gaspare Varvaro: conceptualization, funding acquisition, writing – original draft, writing – review & editing.

## Conflicts of interest

There are no conflicts to declare.

## Data availability

The data supporting this article have been included as part of the Supplementary Information.

## Acknowledgements

This work has been performed in the framework of the Nanoscience Foundry and Fine Analysis (NFFA- MUR Italy Progetti Internazionali) project (www.trieste.NFFA.eu) and has received funding from the European Union's Horizon 2020 Research and Innovation Programme under Project SINFONIA, Grant 964396. The support of Diamond Light Source, instrument I09 (proposal SI32921-1), is gratefully acknowledged. G. V. and D. P. acknowledge the support from the Italian Ministry Research (MUR) under the PRIN program, project No. 2020PY8KTC. G. P. thanks Next Generation EU funds under the Italian Ministry of University and Research (MUR) National Innovation Ecosystem grant ECS00000041 - VITALITY- CUP B43C22000470005. Financial support from the Research Subsidy No. 16.16.110.663 of the AGH University of Krakow is acknowledged (B. R.). We thank Andrea Fondacaro for technical support and fruitful discussions. D.P. and G.V. thank Mr. Enrico Patrizi for his assistance with the magnetic measurements.

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Nanoscale Accepted Manuscript
The data supporting this article have been included as part of the *Supplementary Information*.

DOI: 10.1039/D6NR00971E

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