# Manipulation of artificial multiferroics using doping-induced plastic strain relaxation

Céline Blaess, Pamella Vasconcelos Borges Pinho, Jean-Baptiste Moussy,

Alina Vlad, Christophe Gatel, Sylvia Matzen, Antoine Barbier

► To cite this version:

Céline Blaess, Pamella Vasconcelos Borges Pinho, Jean-Baptiste Moussy, Alina Vlad, Christophe Gatel, et al.. Manipulation of artificial multiferroics using doping-induced plastic strain relaxation. Applied Surface Science, 2025, 690, pp.162585. 10.1016/j.apsusc.2025.162585. hal-04999155

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Submitted on 12 Jun 2025

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Full Length Article

# Manipulation of artificial multiferroics using doping-induced plastic strain relaxation

<figure><img src="image_3.png" /></figure>

Céline Blaess<sup>a</sup>, Pamella Vasconcelos Borges Pinho<sup>b,c,*</sup>, Jean-Baptiste Moussy<sup>a</sup>, Alina Vlad<sup>d</sup>, Christophe Gatel<sup>e</sup>, Sylvia Matzen<sup>f</sup>, Antoine Barbier<sup>a</sup>

## ARTICLE INFO

### Keywords:

Oxynitrides

Artificial multiferroics

Strain relaxation

Epitaxial heterostructures

Opto-spintronics

## ABSTRACT

In this work, we present a comprehensive and comparative study on the growth and magnetic properties of CoFe₂O₄ layers deposited on both undoped and self-oxidized N-doped BaTiO₃ films grown on La₂/₃Sr₁/₃MnO₃/SrTiO₃ (001) substrates, a prototypical magneto-electric multiferroic system. The oxide layers were grown by plasma-assisted molecular beam epitaxy. We show that N doping, even at a low level of 1 %, induces substantial changes in growth modes and strain relaxation in BaTiO₃ and consequently in the CoFe₂O₄ top layer, which exhibits enhanced magnetization and reduced magnetocrystalline anisotropy. The magnetic properties were determined from extensive element-specific magnetic X-ray dichroic measurements, which were simulated through crystal field multiplet calculations. The structural properties of the samples were investigated using grazing incidence X-ray diffraction and high-resolution electron microscopy. Our observations provide evidence that the plastic relaxation of the underlying ferroelectric N-doped BaTiO₃ layer affects the magnetic properties of the top CoFe₂O₄ layer and can serve as an additional tuning parameter for manipulating the expected properties of multiferroics.

## 1. Introduction

Over the past few decades, the search for faster, more energy-efficient technologies has driven a growing interest in multifunctional materials to integrate increasingly complex functionalities into ever-smaller devices [1]. In particular, magneto-electric multiferroic materials (i.e., with simultaneous ferroelectric (FE) and ferromagnetic (FM) properties) have attracted much attention since 2007 [2], when the feasibility of a four-state memory encoding information in electric polarization and magnetization was demonstrated. Among the proposed prototypical magnetic ferroelectrics [1,3], the coupling between piezoelectric FE perovskites, such as BaTiO₃ (BTO), and highly magnetosensitive FM spinels, such as CoFe₂O₄ (CFO), shows great potential for spintronic applications [4]. Owing to their large magnetoelectric (ME) coupling between FE and FM phases and their ordering temperatures well above room temperature, epitaxial CFO/BTO thin films are well-documented prototypical systems [5,6,7,8] for studying magnetic states upon multiferroic couplings.

The magnitude of the ME coupling in artificial multiferroics depends strongly on the efficiency of strain transmission across the interface between the two discrete materials. Therefore, it is critically influenced by the quality of the interface [9] and the total strain energy (i.e., intrinsic and extrinsic contributions combined with magnetocrystalline anisotropy, demagnetization, Zeeman, etc.) [10]. The impact of strain on magnetization magnitude and direction during converse ME coupling is closely tied to the control of the initial magnetic anisotropy and the total anisotropy energy. If the total anisotropy energy is too high, the extrinsic strain energy induced by the piezoelectric effect will be insufficient to overcome it, leading to pinned magnetization and consequently reducing or entirely inhibiting the ME coupling. Although different approaches can be used to control magnetic anisotropy [11,12], the response is often still dominated by intrinsic strain. Thus, the growth

<footnote><sup>a</sup> Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France</footnote>

<footnote><sup>b</sup> European Synchrotron Radiation Facility, F-38043 Grenoble, France</footnote>

<footnote><sup>c</sup> Université Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement des Matériaux, 91191 Gif Sur Yvette, France</footnote>

<footnote><sup>d</sup> Synchrotron SOLEIL, BP 48, L'Orme des Merisiers, 91192 Gif-sur-Yvette Cedex, France</footnote>

<footnote><sup>e</sup> CEMES-CNRS, Université de Toulouse, CNRS, 29 rue Jeanne Marvig, 31055 Toulouse, France</footnote>

<footnote><sup>f</sup> Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France</footnote>

<footnote>* Corresponding author at: Université Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement des Matériaux, 91191 Gif Sur Yvette, France.
E-mail address: pamella.vasconcelos@cea.fr (P.V.B. Pinho).</footnote>
mechanism of thin layers in multiferroic artificial heterostructures is of utmost importance, and strain engineering may become a valuable tool for manipulating the properties of magnetoelectric multiferroics, as we will demonstrate here.

In this work, we investigate the impact of nitrogen (N) doping of BaTiO₃ (N:BTO) on the magnetic properties of CoFe₂O₄ top layers in a multiferroic heterostructure (Fig. 1) composed of CFO/N:BTO epitaxially grown on La₂/₃Sr₁/₃MnO₃/SrTiO₃ (001) (LSMO/STO) substrates. Here, the LSMO layer acts as a bottom electrode. The growth of undoped CFO/BTO/LSMO/STO heterostructures has already been described in the literature [9], with BTO showing ferroelectricity and a bulk-like polarization oriented along the out-of-plane direction. In comparison, the crystalline growth of oxynitride thin films and the investigation of their associated physical properties are still in their infancy. In recent works [13,14], we have demonstrated that it is possible to elaborate high-quality 1 % doped N:BTO epitaxial thin films by self-oxidation. Besides changing the growth mechanism of BTO thin films, N-doping offers several advantages such as improved photoelectrochemical properties [13], larger optical window, and higher photocatalytic activity [15], while keeping its ferroelectric behavior [14]. Moreover, the additional control over the electronic and optical properties of the films may open pathways for novel applications in different fields such as optoelectronics.

Since the growth of prototypical multiferroic heterostructures with tunable optical properties is a key technology for modern applications in photocatalysis [16,17] or optoelectronic devices [18], we propose here a comprehensive study on the growth of CFO on both undoped and N-doped BTO/LSMO/STO substrates. The chemical, structural and magnetic properties of these heterostructures will be compared. The aim is to separate the effects of composition (i.e., cationic arrangement in the octahedral and tetrahedral sites of the spinel structure, as shown in Fig. 1) from strain effects, as both can dramatically alter the magnetic properties of CFO thin films. We demonstrate that undoped BTO grows in a *quasi* layer-by-layer manner, resulting in strained layers due to the clamping effect of the substrate induced by the lattice misfit. In contrast, the self-oxidation growth mechanism of N-doped BTO promotes a nucleation/coalescence island growth mode, in which strain in the growing films is released through plastic relaxation (i.e., formation of defects, such as dislocations and low-angle grain boundaries). In fact, the CFO layers grown on these heterostructures exhibit different structural parameters: they are slightly tetragonal when grown on the former and cubic when grown on the latter. Consequently, CFO/BTO displays reduced magnetization and a higher magnetocrystalline anisotropy than CFO/N:BTO. These observations provide evidence that the plastic relaxation of the underlying N:BTO layer positively affects the magnetic properties of the top CFO layer and can be used as an additional tuning parameter to manipulate the properties of multiferroic heterostructures.

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Schematic representation of the CoFe₂O₄/N:BaTiO₃/La₂/₃Sr₁/₃MnO₃/SrTiO₃ (001) artificial multiferroic heterostructure. Here, the octahedral sites (green) and tetrahedral sites (blue) of the spinel structure are highlighted.</figcaption></figure>

## 2. Experimental section

### 2.1. Multilayer design

The layers of CoFe₂O₄/N:BaTiO₃ (or BaTiO₃)/La₂/₃Sr₁/₃MnO₃/SrTiO₃ heterostructures were elaborated using physical vapor deposition methods. First, a La₂/₃Sr₁/₃MnO₃ (LSMO) layer was epitaxially grown on (001)-oriented SrTiO₃ (STO) substrates by pulsed laser deposition (Nd:YAG laser, wavelength λ = 355 nm, laser frequency = 2.5 Hz, pulse duration time = 15 ns). Then, on the top of LSMO/STO, stoichiometric BaTiO₃ (BTO) or 1 % N-doped BaTiO₃ (N:BTO) were grown by molecular beam epitaxy (MBE). During the growth, the metal evaporation rate was fixed at 0.73 Å·min⁻¹ for both Ba and Ti after in situ calibration with a quartz balance. While the deposition of BTO was assisted by an oxygen plasma (O-MBE setup), the deposition of N:BTO was assisted only by a nitrogen plasma (N-MBE setup). Therefore, the N:BTO layer grows by self-oxidation, i.e. the O atoms migrate from the substrate to the growing film, as shown in our previous studies [13,14]. Finally, to complete the assembly, the ferrimagnetic CoFe₂O₄ (CFO) layer was deposited by O-MBE. Its growth is performed immediately after deposition of the N:BTO (or BTO) layers in order to avoid any surface contamination. The metal evaporation rate was fixed at 0.15 Å·min⁻¹ and 0.30 Å·min⁻¹ for Co and Fe, respectively. By adjusting the deposition times of each layer, a stack of approximately 10 nm of LSMO, 10 nm of N:BTO (or BTO), and 10 nm of CFO was obtained. More information on the growth of each layer in the stack is provided in the Supporting Information.

### 2.2. Multilayer characterization

The crystalline structure of the growing oxide layers was followed in real-time using a reflection high-energy electron diffraction (RHEED) setup. Following the growth, various characterization techniques were combined to obtain physical, chemical and structural information on the thin films. The stoichiometry and electronic structure of the layers were verified in situ by X-ray photoemission spectroscopy (XPS) measurements using a PHOIBOS 100 MCD-5 spectrometer with a Mg Kα source (hv = 1254 eV). The data were treated with the CasaXPS software [19].

The crystalline structure and the epitaxial relationship between the films were confirmed by grazing incidence X-ray diffraction (GIXRD). The measurements were performed using the MED end-station of the Surfaces and Interfaces X-ray Scattering (SixS) beamline at Synchrotron SOLEIL at a photon energy of 15.59 keV (wavelength 0.0795 nm). The diffraction data were collected using a XPAD S140 two-dimensional hybrid pixel detector [20] and the BINoculars software [21] was used to reconstruct the reciprocal space maps (RSM). The reciprocal space coordinates (HKL) are defined in the (a*, b*, c*) basis of the reciprocal lattice of cubic SrTiO₃. Specular scans were used to determine the out-of-plane c parameter, while in-plane scans were used to determine the in-plane a parameter. The residual lattice strain was probed by reciprocal space mapping performed around the (113) Bragg peak of the substrate. The single crystalline quality of the layers was confirmed by 360° RSM measurements carried out for different values of L, corresponding to the Bragg peaks of each type of layers. The mosaicity and the size of crystal domains for the different layers of the sample were deduced from the evolution of the full width at half maximum (FWHM) of the peaks with respect to the in-plane momentum transfer.

The film microstructure was investigated by high-resolution transmission electron microscopy (HRTEM) performed at the CEMES-CNRS laboratory. High-resolution images were recorded using the I2TEM microscope, an Hitachi HF3300-C TEM operating at 300 kV and fitted with a cold field emission gun and an image aberration corrector (BCOR from CEOS) enabled a spatial resolution of 87 pm in high resolution mode. All images were recorded with a direct electron camera (K3 from Gatan Inc). Cross-sectional samples were prepared using Focused Ion Beam (FIB, Ga + source, Helios 600i) by cutting along the [001]
crystallographic directions before thinning by ion milling in order to achieve electron transparency. Sample preparation was completed with low energy cleaning to minimize damage to the surface layers.

After describing structural and chemical properties of the heterostructures, the fine structure and the element-specific magnetic behavior of the CFO top layers were studied. The Fe and Co cation site distribution was determined by exploring the L₂,₃-edges X-ray absorption (XAS) and circular dichroism (XMCD) spectra. The absorption signal was recorded in total electron yield (TEY) mode. The samples were saturated with a magnetic induction of ±5.0 T parallel to the wave vector of the incident photons. Spectra were acquired at room temperature with an angle of 60° between the beam and the sample surface. In addition to the cation site distribution, the magnetic behavior of CFO was also studied using field-dependent XMCD hysteresis loops at Fe and Co L₂,₃-edges. This technique is both element- and site-specific and therefore unbiased by the magnetic contributions of the underlying LSMO layer. The loops were recorded at room temperature and at T = 4 K in both normal and grazing incidences between -5 T and +5 T. All XAS and XMCD measurements were performed in UHV conditions (base pressure of about 10⁻¹¹ mbar) at the European Synchrotron Radiation Facility (ESRF) on beamline ID32 [22].

## 2.3. Crystal field multiplet simulations

To aid in the interpretation of the dichroic spectra, curves for each cation species were simulated with the Crystal Field Multiplet (CFM) model using the quantum many-body script code QUANTY [23,24,25] within the CRISPY [26] graphical interface. Here, we considered independent contributions for the Co (Co<sub>O</sub><sup>2+</sup>, Co<sub>T</sub><sup>2+</sup>, Co<sub>O</sub><sup>3+</sup>, Co<sub>T</sub><sup>3+</sup>) and Fe (Fe<sub>O</sub><sup>2+</sup>, Fe<sub>T</sub><sup>3+</sup>, Fe<sub>O</sub><sup>2+</sup> and Fe<sub>T</sub><sup>2+</sup>) sites where the O and T subscripts stand for octahedral and tetrahedral sites respectively. The atomic parameters for each cation species (see Table A1, Supporting Information) were optimized to improve the fit of the spectra and are in good agreement with the literature [27,28,29]. For all simulated spectra, the ground state was populated according to a Boltzmann distribution at 300 K. The XAS spectra were calculated by solving Green's functions in second quantization. The resulting sharp peaks were convoluted with a Lorentzian function (FWHM = 0.3 eV for L₃ edge and 0.5 eV for L₂ edge) and a Gaussian function (FWHM = 0.5 eV) to mimic the experimental broadening of the spectral lines. The weighting factors for each Co and Fe contribution to the XMCD spectrum were determined using least-squares minimization and curve fitting included in the LMFIT [30] Python package.

# 3. Results

## 3.1. Epitaxial growth and structural characterization

Two sets of heterostructures were prepared: stoichiometric CFO (001) grown on the top of N:BTO/LSMO/STO(001) and BTO/LSMO/STO(001) multilayers. Numerous characterization techniques have been employed to confirm the high purity and single-crystalline nature of each layer of the heterostructures. The focus here is on (i) the growth and characterization of the CFO ferrimagnetic top layer and (ii) the influence that the N:BTO growth mechanism has on its structure and, subsequently, on the magnetic properties of the CFO layer deposited on it. More details on the growth optimization of self-oxidized N:BTO on LSMO/STO(001) substrates and the preliminary structural and chemical characterization of these layers can be found in our previous work [14].

Fig. 2a shows RHEED diffraction patterns that were systematically recorded with the primary beam aligned parallel to [100] and [110] azimuths. The top panel shows the RHEED patterns after deposition of 13 nm thick N:BTO on LSMO/STO. The bottom panel shows the RHEED patterns after deposition of 8 nm thick CFO on the former N:BTO/LSMO/STO. Under our growth condition, we obtained well defined strikes with spots for N:BTO, while CFO layers show elongated 3D spots,

<figure><img src="image_5.png" /><figcaption>Fig. 2. Structural characterization of the CoFe₂O₄/N:BaTiO₃/La₂/₃Sr₁/₃MnO₃/SrTiO₃ (001) multilayer. (a) RHEED diffraction patterns of 8 nm thick CFO (bottom figure) grown on 13 nm thick N:BTO (top figure) recorded along the [100] and [110] azimuths. In the bottom right panel, white arrows highlight the additional rods that appear along the [110] azimuth with the growth of the spinel layer. (b) θ-2θ XRD scan of the (00L) peaks of CFO, N:BTO and STO substrate, represented using reciprocal lattice units (r.l.u.) of STO.</figcaption></figure>

indicating that the layer stacking progressively favored island growth-mode. The patterns are however well contrasted and demonstrate the epitaxial growth of (001)-oriented layers of N:BTO within a perovskite structure and of CFO within a spinel structure. Because the spinel lattice parameter ($a_{bulk}$ = 0.8392 nm, space group *Fd$\overline{3}$m at 298 K) is nearly twice that of BTO ($a_{bulk}$ = 0.3992 nm, $c_{bulk}$ = 0.4036 nm, space group *P*4mm at 298 K), the ferrite top layer exhibits additional rods along the [110] azimuth [31], highlighted by white arrows in Fig. 2a. These extra rods appear along the first 2 nm of growth, persist and intensify as deposition proceeds, indicating that the film retains its spinel structure throughout the entire growth. They are therefore not due to any reconstruction, as was later confirmed by XRD measurements (Fig. 2b). Furthermore, the evolution of the relative RHEED strike spacing as a function of deposition time (Fig. A1) shows that the CFO remains pseudomorphic to the N:BTO for the first nanometers grown, then the in-plane parameter relaxes after three nanometers. The RHEED diffraction patterns of CFO grown on undoped BTO (Fig. A2) show similar trends, although a fully relaxed state is achieved at greater film thicknesses.

Following the growth, the epitaxial relationship between the different layers of the heterostructure was confirmed by XRD measurements performed at room temperature. As shown in Fig. 2b, θ-2θ XRD
patterns exhibit only (00L) Bragg peaks corresponding to the (001) orientation of the perovskite and spinel structure, indicating the single-phase and single orientation quality of these layers. By fitting the (00L) Bragg peaks with a Gaussian function, we obtained an average out-of-plane lattice parameters (c) thanks to the different diffraction orders. For the CFO/N:BTO/LSMO/STO(001) heterostructure, we found $c_{N:BTO} = 0.4048$ nm and $c_{CFO} = 0.8381$ nm. In-plane parameters (a) were obtained by grazing incidence XRD measurements (Fig. A3) performed along the [0K0] and [HH0] directions under an incidence angle corresponding to the critical angle for total external reflection i.e. 0.15° at the photon energy used. We found $a_{N:BTO} = 0.4001$ nm and $a_{CFO} = 0.8384$ nm. Measurements taken at different angles of incidence (not shown) exhibited no change in the diffraction peak positions and therefore in the value of the lattice parameters. This indicates that the layers are well stratified and relaxed at depth, which is in good agreement with the evolution of the relative RHEED strike spacing during growth. Similar XRD results were obtained for CFO grown on undoped BTO layers, for which we found $c_{BTO} = 0.4064$ nm, $a_{BTO} = 0.3988$ nm, $c_{CFO} = 0.8393$ nm, and $a_{CFO} = 0.8360$ nm. For both heterostructures, the lattice parameter values are fairly close to those expected from their bulk counterparts. However, in the case of CFO grown on BTO, the lattice parameter c is slightly larger than a, resulting in a slight tetragonal deformation ($c/a > 1$).

The layer-substrate and layer-layer interfaces were also evaluated by high-resolution transmission electron microscopy (HRTEM). Fig. 3 depicts HRTEM micrographs of both CFO/N:BTO and CFO/BTO heterostructures with the (001) spinel planes oriented parallel to the substrate surface. Here, the film thicknesses, initially estimated by the growth rate, were confirmed. Fig. 3a shows that a 6.5 nm thick LSMO layer is covered by 13 nm N:BTO layer and 7.5 nm CFO layer. Fig. 3b shows a 10 nm thick LSMO layer covered by 12.5 nm BTO. A 6.5 nm thick CFO completes the stack. All layers exhibit overall good crystalline quality. We observe well defined interfaces between the layers with no noticeable parasitic phases at atomic scale. A wider view of these heterostructures (Fig. A4) shows that some areas of the HRTEM images display slight undulations, especially for CFO/N:BTO. Indeed, the self-oxidation method used to grow the oxynitride layer favors incomplete coalescence of the islands, with some voids in some areas, or local ripples. As a consequence, the top CFO layer is rougher, which is consistent with the

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** High-resolution TEM images of (a) CoFe₂O₄/N:BaTiO₃/La₂/₃Sr₁/₃MnO₃/SrTiO₃ (001) and (b) CoFe₂O₄/BaTiO₃/La₂/₃Sr₁/₃MnO₃/SrTiO₃ (001) multilayers, recorded along the [100] direction.</figcaption></figure>

elongated 3D spots observed in the RHEED patterns. For CFO/BTO films, the BTO layer exhibits higher crystalline quality, as it is grown in a *quasi* layer-by-layer mode. Hence, the top CFO layer is less rough, and the interfaces are better defined. The consequences of the observed structural differences between CFO/BTO and CFO/N:BTO multilayers will be discussed in detail later.

## 3.2. Chemical characterization of CoFe₂O₄ top layers

Once it was confirmed that the multilayers had the desired crystal structure, in situ photoemission spectra (XPS) were acquired. Fig. 4a depicts the XPS survey spectrum for CFO/N:BTO layers, revealing the presence of Co, Fe and O elements. Since XPS probes only the extreme surface (i.e. top 5 nm), characteristic Ba and Ti lines cannot be distinguished. No inhomogeneity or impurities were observed on the heterostructure surface. Similar XPS spectra were obtained for CFO grown on undoped BTO layers (not shown here).

Fig. 4b–c show high resolution XPS spectra of Fe 2p and Co 2p core-levels, respectively. One recognizes two single asymmetrical peaks corresponding to 2p₃/₂ and 2p₁/₂ spin-orbit split components, shake-up satellites and O<sub>KLL</sub> Auger peak (centered at 742 eV). Here, the 2p₃/₂ and 2p₁/₂ envelopes were fitted based on contributions from the tetrahedral (T) and octahedral (O) sites of the spinel structure [32], after Shirley background subtraction. First, by evaluating the relative intensities between the Fe and Co 2p core-levels (including T- and O-sites and satellites), we found a Co:Fe ratio of approximately 0.5, as expected. Then, by evaluating the peaks positions, we confirmed that the cations presented the valences expected for stoichiometric CFO. The Fe 2p₃/₂ and 2p₁/₂ envelopes are centered at 711 eV and 725 eV, respectively. Their associated satellite peaks are located 8 eV above the main peaks. Meanwhile, Co 2p₃/₂ and 2p₁/₂ envelopes are centered at 781 eV and 796 eV, respectively. Their associated satellite peaks are located 6 eV above the main peaks. Such chemical shifts and satellite positions are typical of cobalt ferrites with predominantly Fe³⁺ and Co²⁺ cations [33].

Following [32], we deduced the spinel inversion parameter from the occupation percentage of cobalt at O-sites. From the fit of Co 2p spectra, this percentage was found to be 85 %. XPS analyses are essential in determining the optimized growth conditions for CFO, as they confirmed that the films have the proper stoichiometry and cation oxidation states. Although this technique provides reliable elemental quantitative analysis, it is not the most suitable for quantifying the cation site distribution. The estimation of the spinel inversion parameter was thus confirmed by complementary analyses, as shown in the following section.

## 3.3. Fine structure characterization of CoFe₂O₄ top layers

The cationic repartition in our CFO/N:BTO and CFO/BTO thin films was quantified via X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) measurements at Co and Fe L₂,₃-edges. XAS spectra ($\sigma^{XAS}$) are the average of the circular ($\sigma^+$ and $\sigma^-$) absorption cross sections, while XMCD spectra ($\sigma^{XMCD}$) are differences between the two. Fig. 5 depicts XAS (upper panel) and XMCD (lower panel) spectra of CFO grown on N:BTO (left panel) and undoped BTO layers (right panel). Overall, spectra of both multilayers depict the line shapes of a typical inversed spinel with predominately Co²⁺ and Fe³⁺ species, as previously described in the literature [27,32,34].

The Co L₂,₃-edges XAS and XMCD spectra (Fig. 5a) are divided in the spin-orbit split L₃ (~778 eV) and L₂ (794 eV) parts. Since the CFO top layers are relatively thin (less than 10 nm-thick), the Ba L₃ (~784 eV) and L₂ (~799 eV) edges from the underlying N:BTO (or BTO) layer can also be observed in the XAS spectra. However, as a non-magnetic cation, Ba²⁺ does not give any dichroic signal and the XMCD spectra recorded in this energy range are exclusively from the Co species. The Co L₃-edge has a complex line shape with distinguishable four peaks (A₁-A₄). According to CFM calculations, negative peaks A₁ (776.7 eV), A₃ (778.5 eV) and A₄
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Chemical characterization of 8 nm thick CoFe₂O₄ grown on N:BaTiO₃/La₂/₃Sr₁/₃MnO₃/SrTiO₃ (001). At right, (a) XPS survey spectrum depicting the Fe, Co and O contributions. Zoom on the (b) Fe 2p and (c) Co 2p regions. The contributions of O-sites (green line) and T-sites (blue line) were determined after background treatment (gray line) and subtraction of the O<sub>KLL</sub> Auger peak (red line) and charge transfer satellites (yellow line).</figcaption></figure>

(779.4 eV) can be described properly using only Co²⁺ ions at O-sites (CoO²⁺, light green shade). However, in order to reproduce positive peak A₂ (777.7 eV) well, contributions from Co²⁺ ions at T-sites (CoT²⁺, light blue shade) must be considered. The opposite signs of features A₂ and A₃ confirms the antiparallel alignment between magnetic moments in T- and O-sites of the spinel structure. For both CFO/N:BTO and CFO/BTO multilayers, a good description (χ² = 0.2) of the relative intensities between peaks A₁ to A₄ is obtained when 12% of the Co ions are present in tetrahedral sites. This gives an inversion parameter (y) of about 0.9, which is in good agreement with previous results from photoemission spectra (Fig. 4) and the literature [27].

Like the Co spectra, the Fe spectra (Fig. 5b) are also divided in the spin-orbit split L₃ (~709 eV) and L₂ (~722 eV) parts and display the multiplet structure typical of the ionic nature of iron. The spectral shapes are complex and cannot be described with only one symmetry. According to CFM calculations, the Fe L₃-edge can be decomposed in three distinct contributions (B₁–B₃). Negative peaks B₁ (707.8 eV) and B₃ (709.5 eV) can be described properly by Fe³⁺ ions at O-sites (FeO³⁺, dark green shade), whereas the positive peak B₂ (708.9 eV) comes from Fe³⁺ ions at T-sites (FeT³⁺, dark blue shade). Then again, the opposite sign of the B₁/B₃ and B₂ features results from the antiferromagnetic interaction of Fe ions at O- and T-sites. For both CFO/N:BTO and CFO/BTO multilayers, the intensity and shape of the dichroic experimental spectra are well reproduced (χ² = 0.1) by a FeT³⁺: FeO³⁺ ratio of 2:3 instead of 1:1, as in an ideal spinel structure. This result supports the conclusion that there is some Co²⁺ displaced in the T-sites.

It is noteworthy that quantitative XAS (or XMCD) analysis has an absolute uncertainty typically evaluated around 10 %. The inclusion of small amounts (up to 8 %) of other species (such as Fe²⁺ and Co³⁺) does not significantly alter the quality of the fit (Table A2 and A3), as shown in Fig. A5. On the contrary, for Fe spectra, the inclusion of small amounts of FeO²⁺ (~5 %) may even slightly improve the description (χ² = 0.09, Table A3) of the B₁ feature and the L₂-edge. Another important point is that the model used here remains relatively simple, since it does

not account for charge transfer effects nor distortions in the cation local symmetry. The choice of a simpler model was made due to its robustness and the smaller number of parameters considered in the fit. However, taking distortions into account could also improve the description of the spectra. This would be relevant, particularly for the CFO/BTO sample, for which preliminary diffraction results showed a slight tetragonal deformation. For this sample, we observe a different L₂:L₃ ratio, so the fit is probably not as accurate as for CFO/N:BTO. This difference could possibly be overcome by considering different crystal field parameters. However, this analysis was not performed here, as the differences are quite small and generally within the accuracy limits of this multi-parametric model. Nonetheless, the results obtained using a simpler fit are already fairly robust and indicate that both samples have the characteristics expected for a cobalt ferrite: mainly oxidation states 2⁺ for Co and 3⁺ for Fe cations and an almost completely inversed spinel structure (y ~ 0.9).

### 3.4. Element-selective magnetism

Besides helping to resolve the cationic distribution in the spinel structure, XMCD spectra can also provide quantitative information on element- and site-specific magnetic properties of the films. Indeed, an assessable dichroic signal can be associated with a non-zero magnetic moment along the light propagation axis and the presence of a ferromagnetic or ferrimagnetic long-range order. A notable advantage of using the XMCD signal over macroscopic methods (e.g., SQUID or VSM) is that it provides a way to compare the magnetism of CFO grown on N:BTO and BTO without considering the underlying LSMO layer, which is also magnetic. In order to study element-selective magnetism of the CFO top layers, we carried out in-plane and out-of-plane element-specific magnetic hysteresis (ESMH) loops at room temperature (Fig. A6) and T = 4 K (Fig. A7). The measurements were performed by recording the XMCD intensity (given in % of XAS) as a function of the magnetic field (from +5T to −5T) at the characteristic energies of 778.5 eV (CoO²⁺) and
<figure><img src="image_8.png" /><figcaption>a) Co L$_{2,3}$-edges</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>b) Fe L$_{2,3}$-edges</figcaption></figure>

<figure><img src="image_10.png" /></figure>

**Fig. 5.** Fine structure characterization of CoFe$_{2}$O$_{4}$ grown on N-doped BaTiO$_{3}$ (left) and BaTiO$_{3}$ (right) layers. Experimental (a) Co and (b) Fe L$_{2,3}$-edges XAS (top) and XMCD (bottom) spectra measured at ±5.0 T and room temperature. The raw XMCD spectra were normalized to the maximum of the XAS signal (given in %). The calculated contribution for each cobalt and iron species is shown for each spectrum: CoO$^{2+}$ (light green), CoF$^{2+}$ (light blue), FeO$^{3+}$ (dark green) and FeF$^{3+}$ (dark blue). The red line depicts the sum of the cation contributions calculated by CFM. In inset, the distribution of Co and Fe species (in %).

709.5 eV (FeO$^{3+}$). The same sign of ESMH loops confirms the parallel alignment between magnetic moments of the cations in O-sites of the spinel structure. As shown in Fig. A6, both CFO/N:BTO and CFO/BTO thin films have an in-plane magnetic easy axis, so only the loops recorded at grazing incidence will be discussed further.

<figure><img src="image_11.png" /></figure>

**Fig. 6** depicts in-plane ESMH loops that are associated with the Co$^{2+}$ (Fig. 6a) and Fe$^{3+}$ (Fig. 6b) at O-sites for CFO grown on N:BTO (purple dots) and BTO (yellow dots). A number of differences can be noted in the values of coercive field, saturation magnetization, and remanent magnetization (M$_{R}$/M$_{S}$) for these multilayers. In general lines, the
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 6.** XMCD hysteresis loops (in % of XAS) at (a) Co L₃-edge (778.5 eV) and (b) Fe L₃-edge (709.2 eV), comparison between CoFe₂ O₄ /N:BaTiO₃ layer (purple) and CoFe₂ O₄/BaTiO₃ layer (yellow) both measured at room temperature and grazing incidence. The curves were normalized by the maximum of the XAS signal and corrected by the pre-edge.</figcaption></figure>

extracted coercive field for CFO/N:BTO (0.2 T) is slightly smaller than for CFO/BTO (0.3 T). The same coercive field is observed for Fe and Co in the CFO sublattices, revealing a strong coupling between these elements, as expected for a spinel ferrite. Conversely, the saturation magnetization and M<sub>R</sub>/M<sub>S</sub> at both sites in CFO/N:BTO are slightly larger than that of CFO/BTO. The magnetic moment strength of the CoO<sub>6</sub><sup>2+</sup> (FeO<sub>6</sub><sup>3+</sup>) cations of CFO/N:BTO is 1.2 (1.5) times greater than that of CFO/BTO, while the M<sub>R</sub>/M<sub>S</sub> ratio is 25 % for the former and 22 % for the latter. Similar results are obtained at T = 4 K (Fig. A7). Because the CFO layers have a similar cation distribution (Fig. 5), the difference observed in the magnetic behavior of the CFO layer grown on N:BTO or BTO cannot be attributed to a change in the spin magnetic moments at O- and T-sites. Conducting a deeper analysis of the structural differences between these two multilayers is therefore of utmost importance.

### 3.5. Reciprocal space maps: Mosaicity and domain size

Thin film relaxation and structure were studied in more detail by grazing incidence RSMs recorded around the (113) reflection of the STO substrate and reported in Fig. 7 where the corresponding BTO, CFO and

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 7.** Reciprocal space maps recorded close to the (113) substrate reflection for (a) CoFe₂ O₄ /N:BaTiO₃ /La₂/₃ Sr₁/₃ MnO₃/SrTiO₃ (001) and (b) CoFe₂ O₄/BaTiO₃/La₂/₃ Sr₁/₃ MnO₃ /SrTiO₃ (001) multilayers.</figcaption></figure>

STO Bragg reflections are indicated. The LSMO signal, however, is not distinguishable as its lattice parameter is very close to (and slightly smaller than) that of STO. As shown in Fig. 7, both the BTO 113 and CFO 226 reflections are located at lower L values than those of the STO substrate. From such datasets, we derive the lattice parameters from the position of the maximum signal of each of the characteristic XRD peaks. N:BTO and BTO results show tetragonality c/a around 1.012 and 1.019, respectively. As expected, the CFO layers grown on top of those perovskites presented cubic (or nearly cubic) lattices with c/a ~ 1.000 and 1.004, respectively. Due to plastic relaxation, the CFO/N:BTO layers exhibit tetragonality very close to their bulk counterparts (i.e. c/a = 1.000 for bulk CFO and 1.012 for bulk BTO). On the contrary, in CFO/
BTO heterostructures, the BTO layers are strained due to the clamping effect and misfit with the substrate, resulting in an increased c/a value compared to bulk BTO. Consequently, the CFO top layer is slightly more strained and exhibits also a larger c/a value than that of the bulk. These results are consistent with the smaller in-plane lattice parameter values (and larger out-of-plane values) measured for BTO and CFO layers in the CFO/BTO heterostructure compared to those in the CFO/N:BTO heterostructure.

To further analyze each layer within the heterostructure individually, 360° RSM measurements were performed at different L values (Fig. 8) and incidence angles (Fig. A8) for both CFO/N:BTO and CFO/BTO (not shown here) multilayers. The L values were selected to correspond to the reciprocal spacing specific to the families of planes of each individual layer in the stack. For an incidence angle equal to the critical angle ($α_C = 0.15°$), L = 0 measurements probe the surface components of the ensemble of the layer (Fig. 8a), while L = 0.975 (Fig. 8b) is more sensitive to the BTO lattice and L = 1.86 (Fig. 8c) to the CFO lattice. Likewise, L = 0 measurements performed at half of the critical angle ($1/2 α_C = 0.075°$ in Fig. A8a) are strongly more sensitive to the CFO top layer, while measurements taken at three times the critical angle (3 $α_C = 0.45°$ in Fig. A8b) are more sensitive to the STO substrate. From the ensemble of these measurements, we were able to determine the mosaic spread and domain size of the different layers of the heterostructures.

In plane RSMs depict reciprocal space Bragg peaks whose widths are expected to be the result of the convolution of the following components: (i) a mosaic spread ($Δω$) that is a constant angular azimuthal opening at any reciprocal momentum $q$ value, (ii) a domain size (D) that leads to a finite width ($Δq$) in reciprocal space for any peak, and (iii) a lattice parameter dispersion ($Δa/a$) that spreads linearly with $q$. Thus, azimuthal in plane scans (at fixed $q$) across the Bragg peaks give access to $Δω$ and D. As depicted in Fig. A9, the 360° RSMs were integrated in order to follow the evolution of the intensity for different values of the radius and therefore for different $q$ values, corresponding to H00 and HH0 type measurements for N:BaTiO$_3$ and CoFe$_2$O$_4$ as a function of the radial angle (from 0 to 360°). The peaks resulting from the integration of the RSMs were fitted with a Gaussian function and the average of the FWHM for each $q$ value was extracted. The mosaic spread ($Δω$) was then obtained by fitting with an affine function the evolution of the FWHM of the peaks ($ω$) as a function of $1/q^2$ (Eq. (1)). The domain size (D) was deduced from the obtained $Δq$ (Eq. (2)).

$$ω^2 = \frac{(Δq)^2}{q^2} + (Δω)^2 \quad (1)$$

$$D = \frac{2π}{Δq} \quad (2)$$

Table 1 summarizes the structural parameters obtained by HRTEM and diffraction measurements for the bilayers prepared on the top of LSMO/

STO(001). The in-plane mosaic spread obtained for both CFO($Δω = 1.33°$)/N:BTO($Δω = 1.23°$) and CFO($Δω = 1.78°$)/BTO($Δω = 2.02°$) is rather low for such thin epitaxial oxide films indicating a rather good overall crystalline quality of the epitaxial layers and a clear cube on cube epitaxial relationship free from texturing or polycrystalline contributions. Furthermore, we can note domain sizes (D) of about 10 nm for both N:BTO(D = 11.6 nm)/CFO(D = 9.5 nm) and BTO(D = 15.7 nm)/CFO(D = 6.4 nm) layers. The domain size can be pictured as resulting from the typical distance in the material where the X-rays will be scattered by defects, breaking up the coherence of a single crystalline domain. Smaller domains are observed for the top CFO layers because they are thinner, rougher, and contain multiple grain boundaries, as shown by HRTEM images (Fig. 3). One may however note that in the N: BTO case the CFO top layer adopts almost the structural parameters ($Δω$ and D) of the N:BTO layer, while for the BTO case the CFO domain size is strongly reduced. This is likely due to the difficulty to induce tetragonality in the ferrite lattice in addition to the lattice misfit accommodation. This observation is consistent with the positive role of plastic relaxation in the strain release mechanism; allowing layers to reach faster (in terms of layer thickness) bulk like configurations. As shown in Fig. A1, the a lattice parameter relaxes after the deposition of 3 nm of CFO on N:BTO, whereas deposition on undoped BTO requires approximately 15 nm of CFO to achieve full structural relaxation, as demonstrated in previous studies [7].

## 4. Discussion

Although both CFO layers, grown on 1 % N-doped BTO and undoped BTO, have high crystalline quality (Fig. 3) and the same chemical composition (Fig. 5), these heterostructures exhibit different magnetic behaviors: CFO/BTO displays reduced magnetization and more pronounced magnetocrystalline anisotropy than CFO/N:BTO. Because the CFO layers have a similar cation distribution, such a difference cannot be attributed to a change in the spin magnetic moments at O- and T-sites. However, it could be explained by a change in the ferro- and antiferromagnetic interactions. Indeed, exchange interactions are highly sensitive to cationic distances, which differ in CFO/BTO due to the tetragonal deformation (Fig. 7), contrarily to the CFO/N:BTO case. In fact, the difference in growth mechanisms of N:BTO and undoped BTO has an impact on the structural parameters of the CFO layers grown on the top of them. The self-oxidation method used to grow the N:BTO favors incomplete coalescence of the islands. Thus, due to plastic relaxation (i.e. formation of defects, such as dislocations and low-angle grain boundaries), the N:BTO and CFO layers are nearly completely relaxed. Indeed, XRD measurements (Table 1) show a slight shrinkage of the spinel lattice and a slight expansion of the perovskite lattice (by about 0.2 %) compared to bulk. Since the CFO grown on N:BTO has a cubic structure, its hard axis is less well-defined (Fig. A6), resulting in a less anisotropic layer. In contrast, CFO/BTO layers are grown in a quasi

<figure><img src="image_16.png" /><figcaption>Fig. 8. Reciprocal space maps at 360° recorded with incidence angle equals to the critical angle ($α_C = 0.15°$) for CoFe$_2$O$_4$ /N:BaTiO$_3$ /La$_{2/3}$ Sr$_{1/3}$ MnO$_3$ /SrTiO$_3$ (001) layers. Here, (a) L = 0 measurements probe the surface components of the ensemble of the heterostructure, while (b) L = 0.975 is more sensitive to the N: BaTiO$_3$ lattice and (c) L = 1.86 to the CoFe$_2$O$_4$ lattice.</figcaption></figure>
<caption>**Table 1**</caption>

Summary of the structural parameters obtained for the different heterostructures synthesized: thickness (d), tetragonality (c/a), mosaicity (Δω) and domain sizes (D).

<table><thead><tr><th>heterostructure</th><th>layer</th><th>d (nm)</th><th>a (nm)</th><th>c (nm)</th><th>c/a</th><th>Δω (°)</th><th>D (nm)</th></tr></thead><tbody><tr><td rowspan="2">CFO/N:BTO/LSMO/STO</td><td>N:BTO</td><td>13</td><td>0.4001</td><td>0.4048</td><td>1.012</td><td>1.23 ± 0.07</td><td>11.6 ± 0.5</td></tr><tr><td>CFO</td><td>7.5</td><td>0.8384</td><td>0.8381</td><td>1.000</td><td>1.3 ± 0.1</td><td>10 ± 1</td></tr><tr><td rowspan="2">CFO/BTO/LSMO/STO</td><td>BTO</td><td>12.5</td><td>0.3988</td><td>0.4064</td><td>1.019</td><td>2.02 ± 0.09</td><td>16 ± 2</td></tr><tr><td>CFO</td><td>6.5</td><td>0.8360</td><td>0.8393</td><td>1.004</td><td>1.8 ± 0.3</td><td>6.4 ± 0.8</td></tr></tbody></table>

layer-by-layer mode. In this case, we observe a network of misfit dislocations that contributes to the partial relaxation of the layers. However, a compressive in-plane strain persists and CFO/BTO is slightly tetragonal due to the misfit and clamping effect of the substrate. This leads to a gain of anisotropy and a decrease in magnetic moment (Fig. A6).

A change in the ferromagnetic long-range order should also be considered. Indeed, as it was shown for magnetite [35,36], the magnetic behavior in epitaxial thin films can be influenced by the presence of antiphase boundaries (APBs). Since the magnetic coupling across an APB tends to be antiferromagnetic [37], a high density of APBs may reduce the average magnetic moment of the thin film. According to the literature [38], the APB density usually decreases as the domain size increases. Consequently, the smaller domain size in CFO shown for CFO/BTO (D = 6.4 ± 0.8 nm), as compared to CFO/N:BTO (D = 10 ± 1 nm), also plays a role in the differences in magnetic behavior observed between these CFO layers. However, since the thicknesses of the multilayers are very similar (d ~ 7 nm) and the domain sizes remain small, the effect of the residual strain and tetragonal deformation are expected to have a predominant impact on the magnetic crystalline anisotropy, as has been demonstrated in previous works [39] and the literature [10,40]. Even though it is very challenging to disentangle the effect of these structural parameters.

To conclude, it is important to highlight that the initial magnetic anisotropy of the spinel ferrimagnetic layer is a crucial parameter influencing the magnetoelectric properties of this prototypical artificial multiferroic heterostructure. As shown in the literature [10], if the total anisotropy energy is too high, the extrinsic strain energy induced by the piezoelectric effect will be insufficient to overcome it. This results in pinned magnetization, thereby hindering the magnetoelectric coupling.

## 5. Conclusions

In the present work, we compared two multiferroic heterostructures that differ mainly by the inclusion of N doping (ca. 1%) within the ferroelectric BTO layer. When BTO is grown under N-plasma, self-oxidation occurs due to the migration of O atoms from the underlying LSMO/STO substrate. Although chemically very similar to a layer grown under O-plasma, we demonstrated slight structural changes and clear modifications in growth mode, which tends more toward nucleation/coalescence compared to the layer-by-layer behavior of pure BTO. This results in a relaxed heterostructure for the CFO/N:BTO case, with similar layer thicknesses, exhibiting stronger magnetism and lower magnetocrystalline anisotropy. More generally, we believe that this work demonstrates that strain relaxation engineering, even with small doping levels, is a potential route to manipulate the magneto-electric response of multiferroic heterostructures.

### CRediT authorship contribution statement

**Céline Blaess:** Writing – review & editing, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.
**Pamella Vasconcelos Borges Pinho:** Writing – original draft, Validation, Methodology, Investigation, Formal analysis, Data curation.
**Jean-Baptiste Moussy:** Writing – review & editing, Methodology, Investigation, Data curation.
**Alina Vlad:** Writing – review & editing, Methodology, Formal analysis, Data curation.
**Christophe Gatel:** Writing –

review & editing, Methodology, Formal analysis, Data curation. **Sylvia Matzen:** Writing – review & editing, Methodology, Formal analysis, Data curation, Conceptualization.
**Antoine Barbier:** Writing – original draft, Validation, Supervision, Methodology, Funding acquisition, Formal analysis, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: [Antoine Barbier reports financial support was provided by French National Research Agency. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper].

### Acknowledgements

This work was funded by the French National Research Agency (ANR) through MULTINANO project (Grant ANR19-CE09-0036). The synchrotron experiments were performed at ESRF and SOLEIL Synchrotron facilities under proposal numbers IH-HC-3857 (DOI: 10.15151/ESRF-ES-1069361361) and 20221566, respectively. We acknowledge ESRF and SOLEIL for provision of synchrotron radiation facilities and we would like to thank the beamline staff for assistance in using beamlines ID32 and SIXS.

## Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.apsusc.2025.162585.

### Data availability

Data will be made available on request.

### References

[1] N. Ortega, A. Kumar, J.F. Scott, R.S. Katiyar, Multifunctional magnetoelectric materials for device applications, J. Phys. Condens. Matter 27 (50) (2015) 504002, https://doi.org/10.1088/0953-8984/27/50/504002.

[2] M. Gajek, et al., Tunnel junctions with multiferroic barriers, Nat. Mater. 6 (4) (2007) 296–302, https://doi.org/10.1038/nmat1860.

[3] C.A.F. Vaz, J. Hoffman, C.H. Ahn, R. Ramesh, Magnetoelectric coupling effects in multiferroic complex oxide composite structures, Adv. Mater. 22 (26–27) (2010) 2900–2918, https://doi.org/10.1002/adma.200904326.

[4] Y. Zhang, Z. Li, C. Deng, J. Ma, Y. Lin, C.-W. Nan, Demonstration of magnetoelectric read head of multiferroic heterostructures, Appl. Phys. Lett. 92 (15) (2008) 152510, https://doi.org/10.1063/1.2912032.

[5] H. Zheng, et al., Multiferroic $BaTiO_3-CoFe_2O_4$ nanostructures, Science 303 (5658) (2004) 661–663, https://doi.org/10.1126/science.1094207.

[6] R.V. Chopdekar, et al., Spatially resolved strain-imprinted magnetic states in an artificial multiferroic, Phys. Rev. B 86 (1) (2012) 014408, https://doi.org/10.1103/PhysRevB.86.014408.

[7] N. Jedrecy, et al., Cross-correlation between strain, ferroelectricity, and ferromagnetism in epitaxial multiferroic $CoFe_2O_4/BaTiO_3$ heterostructures, ACS Appl. Mater. Interf. 10 (33) (2018) 28003–28014, https://doi.org/10.1021/acsami.8b09499.

[8] R.V. Chopdekar, Y. Suzuki, Magnetoelectric coupling in epitaxial $CoFe_2O_4$ on $BaTiO_3$, Appl. Phys. Lett. 89 (18) (2006) 182506, https://doi.org/10.1063/1.2370881.
[9] N. Dix, et al., Large out-of-plane ferroelectric polarization in flat epitaxial BaTiO₃ on CoFe₂O₄ heterostructures, Appl. Phys. Lett. 102 (17) (2013) 172907, https://doi.org/10.1063/1.4803943.

[10] L.M. Garten, M.L. Staruch, K. Bussmann, J. Wollmershauser, P. Finkel, Enhancing converse magnetoelectric coupling through strain engineering in artificial multiferroic heterostructures, ACS Appl. Mater. Interf. 14 (22) (2022) 25701–25709, https://doi.org/10.1021/acsami.2c03869.

[11] E. Freeman, et al., Improving the magnetoelectric performance of Metglas/PZT laminates by annealing in a magnetic field, Smart Mater. Struct. 26 (8) (2017) 085038, https://doi.org/10.1088/1361-665X/aa770b.

[12] B. Bagyalakshmi, M.V. Gajendra Babu, B. Sundarakannan, S. Kalavathi, V. Sridharan, G. Amarendra, Converse magnetoelectric effect in NiFe₂O₄/BaTiO₃ heterostructure by electric field induced inter-ferroelectric phase transition, Mater. Lett. 170 (2016) 48–52, https://doi.org/10.1016/j.matlet.2016.01.140.

[13] A. Derj, H. Magnan, C. Mocuta, P. Le Fèvre, J. Leroy, A. Barbier, Properties of self-oxidized single crystalline perovskite N:BaTiO₃ oxynitride epitaxial thin films, Mater. Adv. 3 (7) (2022) 3135–3142, https://doi.org/10.1039/D1MA01082D.

[14] C. Blaess, et al., Nitrogen doping in epitaxial self-oxidized BaTiO₃ ferroelectric thin films: from chemical to optical properties, J. Phys. Chem. C (Under Revision) (2025).

[15] J. Cao, Y. Ji, C. Tian, Z. Yi, Synthesis and enhancement of visible light activities of nitrogen-doped BaTiO₃, J. Alloy. Compd. 615 (2014) 243–248, https://doi.org/10.1016/j.jallcom.2014.07.008.

[16] S. Mohan, B. Subramanian, I. Bhaumik, P.K. Gupta, S.N. Jaisankar, Nanostructured Bi(1-x)Gd(x)FeO₃ – a multiferroic photocatalyst on its sunlight driven photocatalytic activity, RSC Adv. 4 (32) (2014) 16871–16878, https://doi.org/10.1039/C4RA00137K.

[17] X. Zhang, Y. Zhang, F. Yang, J. Zhang, Y. Liu, S. Li, Magnetic field driven catalysis of multiferroic magnetoelectric nanocomposites, Mater. Lab 3 (1) (2024) 230025, https://doi.org/10.54227/mlab.20230025.

[18] H. Sharifi Dehsari, M. Hassanpour Amiri, K. Asadi, Solution-processed multiferroic thin-films with large magnetoelectric coupling at room-temperature, ACS Nano 17 (9) (2023) 8064–8073, https://doi.org/10.1021/acsnano.2c09769.

[19] N. Fairley, et al., Systematic and collaborative approach to problem solving using X-ray photoelectron spectroscopy, Appl. Surf. Sci. Adv. 5 (2021) 100112, https://doi.org/10.1016/j.apsadv.2021.100112.

[20] A. Dawiec, et al., Real-time control of the beam attenuation with XPAD hybrid pixel detector, J. Instrum. 11 (12) (2016) P12018, https://doi.org/10.1088/1748-0221/11/12/P12018.

[21] S. Roobol, W. Onderwaater, J. Drnec, R. Felici, J. Frenken, BINoculars: data reduction and analysis software for two-dimensional detectors in surface X-ray diffraction, J. Appl. Cryst. 48 (4) (2015) 1324–1329, https://doi.org/10.1107/S1600576715009607.

[22] K. Kummer, et al., The high-field magnet endstation for X-ray magnetic dichroism experiments at ESRF soft X-ray beamline ID32, J. Synchrotron Rad. 23 (2) (2016) 464–473, https://doi.org/10.1107/S160057751600179X.

[23] M.W. Haverkort, G. Sangiovanni, P. Hansmann, A. Toschi, Y. Lu, S. Macke, Bands, resonances, edge singularities and excitons in core level spectroscopy investigated within the dynamical mean-field theory, Europhys. Lett. 108 (5) (2014) 57004.

[24] M.W. Haverkort, M. Zwierzycki, O.K. Andersen, Multiplet ligand-field theory using Wannier orbitals, Phys. Rev. B 85 (16) (2012).

[25] Y. Lu, M. Höppner, O. Gunnarsson, M.W. Haverkort, Efficient real frequency solver for dynamical mean field theory, Phys. Rev. B 90 (2014).

[26] M. Retegan, “Crispy: version 0.7.3.” 2019. [Online]. Available: https://dx.doi.org/10.5281/zenodo.1008184.

[27] J.F. Hochepied, P. Saintavit, M.P. Pileni, X-ray absorption spectra and X-ray magnetic circular dichroism studies at Fe and Co L₂,₃ edges of mixed cobalt-zinc ferrite nanoparticles: cationic repartition, magnetic structure and hysteresis cycles, J. Magn. Magn. Mater. 231 (2) (2001) 315–322, https://doi.org/10.1016/S0304-8853(01)00182-2.

[28] E. Bartolomé, et al., Magnetic stability against calcining of microwave-synthesized CoFe₂O₄ nanoparticles, New J. Chem. 40 (8) (2016) 6890–6898, https://doi.org/10.1039/C6NJ00705H.

[29] P.V.B. Pinho, et al., Stoichiometry driven tuning of physical properties in epitaxial Fe₃ₓCrₓO₄ thin films, Appl. Surf. Sci. 615 (2023) 156354, https://doi.org/10.1016/j.apsusc.2023.156354.

[30] M. Newville et al., Imfit/lmfit-py: 1.0.3. (Oct. 2021). Zenodo. doi: 10.5281/zenodo.5570790.

[31] C. Mocuta, P. Ohresser, A. Barbier, Chap. 18 - Artificial laminar oxide multiferroic magnetoelectric thin film structures: elaboration methods and study by synchrotron radiation techniques, Mater. Devices 5 (2) (2022).

[32] T. Aghavnian, et al., Determination of the cation site distribution of the spinel in multiferroic CoFe₂O₄/BaTiO₃ layers by X-ray photoelectron spectroscopy, J. Electron Spectrosc. Relat. Phenom. 202 (2015) 16–21, https://doi.org/10.1016/j.elspec.2015.02.006.

[33] M.C. Biesinger, B.P. Payne, A.P. Grosvenor, L.W.M. Lau, A.R. Gerson, R. St, C. Smart, Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni, Appl. Surf. Sci. 257 (7) (2011) 2717–2730.

[34] S. Imada, T. Jo, Magnetic states of cobalt oxide and ferrites and magnetic dichroism in 2p-3d X-ray absorption spectroscopy, J. Magn. Magn. Mater. 104–107 (1992) 2001–2002, https://doi.org/10.1016/0304-8853(92)91641-6.

[35] D.T. Margulies, et al., Origin of the anomalous magnetic behavior in single crystal Fe₃O₄ Films, Phys. Rev. Lett. 79 (25) (1997) 5162–5165.

[36] A.M. Bataille, et al., Characterization of antiphase boundary network in Fe₃O₄ epitaxial thin films: effect on anomalous magnetic behavior, Phys. Rev. B 74 (15) (2006) 155438, https://doi.org/10.1103/PhysRevB.74.155438.

[37] S. Celotto, W. Eerenstein, T. Hibma, Characterization of anti-phase boundaries in epitaxial magnetite films, Eur. Phys. J. B – Cond. Matter 36 (2) (2003) 271–279.

[38] J.-B. Moussy, et al., Thickness dependence of anomalous magnetic behavior in epitaxial Fe₃O₄(111) thin films: effect of density of antiphase boundaries, Phys. Rev. B 70 (17) (2004) 174448.

[39] C. Gatel, B. Warot-Fonrose, S. Matzen, J.-B. Moussy, Magnetism of CoFe₂O₄ ultrathin films on MgAl₂O₄ driven by epitaxial strain, Appl. Phys. Lett. 103 (9) (2013) 092405, https://doi.org/10.1063/1.4819178.

[40] A. Nabialek, et al., Influence of the strain effect on magnetocrystalline anisotropy in Co₂Fe₄Mn₆Si Heusler alloys, Scient. Rep. 13 (1) (2023) 17016, https://doi.org/10.1038/s41598-023-43979-x.