{"paper_id":"00aa1e7d-37dd-412e-a8db-e20f55329d26","body_text":"Local magnetoelectric effect in Fe3O4-BaTiO3 nanocomposites | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Local magnetoelectric effect in Fe 3 O 4 -BaTiO 3 nanocomposites D. A. Kanurin, A. A. Amirov, N. N. Liu, T. R. Nizamov, Yu. A. Alekhina, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5390395/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Apr, 2025 Read the published version in Journal of Nanoparticle Research → Version 1 posted 4 You are reading this latest preprint version Abstract Magnetoelectric nanoparticles (MENPs) are emerging as potential nanomaterials for a wide range of biomedical applications. Recently, many studies have been devoted to investigating the properties of MENPs based on cobalt ferrite. The outstanding magnetic properties of cobalt ferrite nanoparticles, such as higher values of coercive force and magnetostriction coefficient compared to other metal ferrites of spinel structures are well known. However, the biocompatibility and toxicity of cobalt ferrite nanoparticles are still a matter of debate and not fully studied. Therefore, design of MENPs with magnetic core having low toxicity is still a challenging task. Thus, we proposed to use iron oxide nanoparticles (FO) instead of cobalt ferrite as a less toxic alternative. This work represents a comprehensive study of the structural, crystalline, magnetic, and magnetoelectric (ME) properties of synthesized MENPs based on FO and barium titanate (BTO), where FO and BTO provide magnetostrictive and piezoelectric functionalities, respectively. The synthesis of FO of three sizes (12.7, 25.9, 47.7 nm) was carried out, after which the resulting nanoparticles were coated with BTO phase. Samples of all series were characterized by the methods of transmission electron microscopy (TEM), vibrating-sample magnetometry (VSM), X-ray diffraction (XRD) analysis. The longitudinal magnetostriction coefficient was found to be 6.5 ppm for FO with a diameter of 12.7 nm, 6.8 ppm with a diameter of 25.9 nm, and 14.6 ppm with a diameter of 47.7 nm. Piezoresponse force microscopy measurements qualitatively showed a change in the amplitude and phase of the piezoelectric response of MENPs when a magnetic field is applied to the sample. magnetoelectric effect magnetic nanoparticles magnetoelectric nanoparticles multiferroic nanocomposites iron oxide piezoresponse force microscopy magnetostriction. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Introduction Recently, the development and use of brain-computer interfaces (BCIs) — systems for exchanging information between the human brain and electronic devices — has attracted significant attention from researchers [1-3]. Today, BCIs are actively being used to enhance the functionality of prosthetics, restore vision and hearing, regain lost motor abilities, and treat Parkinson's disease, epilepsy, and dystonia [4-6]. However, there are still several limitations that prevent the widespread and effective use of BCIs [7,8]. To fully realize the potential of these interfaces, several important steps must be taken. For broad and long-term use, it is necessary to achieve minimally invasive implantation procedures, biocompatibility of materials for implants, and the safety of stimulating effects [9]. The number of neural channels that the implanted device can access must be increased by several orders of magnitude [10]. Spatial resolution should be equal to or smaller than the diameter of small groups of neurons (i.e., on the micron scale), and temporal resolution should be faster or comparable to that of neurons in the native brain (i.e., response time of less than a millisecond) [11]. In the context of the aforementioned methods and considering the shortcomings of each, the primary focus of researches is the development of compact and safe systems that enable non-invasive “deep” brain stimulation with the prospect of reading signals received from neurons. In this regard, the use of a magnetic field as an external stimulus and composite magnetic nanoparticles (MNPs) for local “deep” effects appears to be very promising and meets the specified conditions [12-14]. The literature describes various approaches MNPs for signal transmission to and recording from neurons. For example, magnetothermal: due to magnetic hyperthermia, the area around the nanoparticle is heated, which can affect the neuron [13, 15-18]. Magneto-mechanical deformation [19]: a potential effect arises from the rotation of magnetic cores with magnetic anisotropy under the influence of a low frequency magnetic field; the mechanical stress on neuron, caused by the rotation, can trigger a transmittance of electrical impulse to another neuron. Magnetostrictive: the use of MENPs (nanocomposites) with a multiferroic nature, with a magnetostrictive core and a piezoelectric shell, is proposed; a potential difference arises on the surface of piezoelectric particles under mechanical stress due to the magnetostriction of the cores when a magnetic field is applied; through the potential difference induced on the particle surface, it is possible to transmit an electrical impulse to the neuron or read it from the neuron [11, 20-24]. Exactly the magnetostrictive approach to deforming the piezoelectric shell and creating a potential on the surface of the MENPs for transmitting information to neurons is considered as promising for neurostimulation in many recent studies. Most of these studies are focused on the properties of MENPs based on cobalt ferrite, which are known for their strong magnetic characteristics compared to other spinel ferrites [22-29]. However, concerns remain regarding the biocompatibility and toxicity of cobalt ferrite nanoparticles, as they are not fully understood [30-32]. To address this, the current work proposes the use of FO with lower toxicity as the magnetostrictive phase of MENPs and BTO as the piezoelectric phase. Study of the structural, crystalline, magnetic, magnetostrictive and ME properties of MENPs for the magnetostrictive approach is the focus of this research. The general idea of this paper is based on the development of method to observe the local piezoresponse in low-toxicity biocompatible MENPs, which are promising for neurostimulation tuning by remotely applied magnetic field as a result of ME coupling. Materials and Methods Chemicals Iron (III) acetylacetonate (Fe(acac) 3 ); triethylene glycol, 99% (TEG); titanium (IV) isopropoxide, 97%; barium hydroxide octahydrate (II) (Ba(OH) 2 •8H 2 O); 1-octadecene, ≥ 95%; oleic acid, ≥ 99% (Roth; Germany); ethyl acetate, ≥99.5%; butanol-1, ≥99.4%; ethanol, ≥ 95%, polyvinylpyrrolidone, 10 kDa (PVP), Pluronic F127, deionized water. All the used chemicals except oleic acid and distilled water were provided by Sigma-Aldrich, USA. Synthesis of the samples The MENPs of Fe 3 O 4 @BaTiO 3 with core-shell like structure, consisted of magnetic core of FO and piezoelectric shell of BTO were synthesized using following stages: thermal decomposition method for core synthesis and solvothermal method for shell synthesis. For this purpose was used the protocol described elsewhere [22, 33]. As a result of the synthesis, three groups of FO nanoparticles FO1, FO2, and FO3, with 3 different core sizes were obtained. The particles from each group were then coated with a BTO shell, resulting in three different samples for further magnetoelectric measurements: FO1@BTO, FO2@BTO, and FO3@BTO. The characterization of the obtained samples is presented in the following chapters. Some of the particles were immediately taken for measurements, the other part was first annealed in a muffle furnace for 5 hours at a temperature of 700 °C. Sample FO2@BTO was grounded in a Retsch MM301 ball mill for 12 hours in 25 ml tungsten carbide bowls using one ball with a diameter of 15 mm and 20 balls with a diameter of 1 mm. To stabilize the particles, octadecene and oleic acid were added to them during grinding. The synthesis process will be detailed in Appendix A. Characterization The morphology of the MENPs was studied using JEM-1400 transmission electron microscope (TEM) (JEOL; Japan) with an accelerating voltage 120 kV. TEM images show the structure of the nanoparticles. MNPs average size was determined using the ImageJ software. For this purpose, the sizes of 100 randomly selected particles from the image were measured, followed by the construction of size distribution histograms. Structure and phase analysis were performed using a STADI P powder diffractometer (STOE, Darmstadt, Germany). The measurements were carried out using an Image Plate detector. The sample preparation was as follows: the sample was ground in an agate mortar in ethanol media. After that, the sample was applied between two films using silicone grease. Both the film and the silicone grease are transparent to XRD radiation in the studied angular range. The film with the sample was then fixed in a cuvette. The X-ray diffraction analysis in the angular range of (20–100)° at room temperature was conducted using the Rietveld method with the FullProf software with a step 0.002°. To study the magnetic properties of the investigated particles, their hysteresis magnetization loops were recorded. Magnetic measurements were carried out using Lakeshore 7407 VSM (Lake Shore Cryotronics, USA) at room temperature. The powdered samples were sealed in polyethylene capsules with approximate dimensions of 4x4x0.5 mm. The capsules were not laminated to prevent sample degradation, and for this reason, the particles could move during the measurements. The capsule was fixed to the holder using a Teflon tape. The magnetic field up to 16 kOe was applied in the plane of the capsule to minimize the influence of the demagnetizing field. The local ME effect was studied using PFM technique with АСМ NTEGRA PRIMA commercial scanning probe microscope. For these measurements, commercial cantilevers HA_HR/W2C, NSG01/Pt, NSG01/TiN were utilized. The sample was suspended in ethanol and then applied to a conductive copper tape. Measurements were carried out both without and with the application of a magnetic field (H = 2 kOe). The magnetic field was applied parallel to the surface of the sample. Magnetostrictive measurements were conducted using self-designed experimental set-up based strain gauges measurements technique. The values of the longitudinal and transverse magnetostriction coefficients of FO nanoparticles were measured before MNPs annealing. The experimental setup and measurement methodology are described in detail in Appendix B. Results and discussion TEM measurements As a result of the synthesis, FO@BTO particles with cores of three different sizes (FO1 with average size D=12.7±1.6 nm, FO2 with average size D=25.9±3.4 nm, FO3 with average size D=47.7±4.3 nm) were obtained (Fig. 1). In this figure, the polycrystalline structure of the obtained MNPs is clearly visible. Figure 2 shows the histograms of nanoparticle size distribution. Suspensions of particles of all sizes demonstrate colloidal stability in triethylene glycol (TEG) over an extended period. However, in the image of FO3 (Fig. 1 c), it can be seen that the MNPs have sufficient residual magnetization to align into chains in a less viscous medium, such as ethanol. Fig. 3 shows an image of the FO@BTO composite. In this image, one can see the BTO matrix, within which particles or clusters of FO nanoparticles are embedded. In such a structure, the magnetoelectric effect should be observed. However, due to the inhomogeneity of the obtained sample, the interaction between the magnetic (FO) and electrical (BTO) subsystems will vary in different areas of the sample. Therefore, in some regions of the sample, AFM measurements should show the presence of surface potential induced by the magnetic field, while in others, they should not. Although the FO3 MNPs demonstrate (as will be shown later) the best magnetic, including magnetostrictive, properties, they tend to clump into chains due to their high spontaneous magnetization (Fig. 1 c). This necessitates additional surface treatment of the particles before coating them with BTO to achieve a uniform coating of the magnetic core with the BTO shell. According to [22], during milling, the composite should break down into individual particles. In Fig. 4, it can be seen that after annealing and milling with stabilizers, the composite breaks down into smaller clusters of about several hundred nanometers in size. For further measurements using probe methods, FO2@BTO sample was selected, as it demonstrates greater stability compared to larger MENPs and superior magnetic properties compared to smaller MENPs. XRD measurements Figure 5 shows the diffractogram of magnetite MNPs powders of different sizes. All peaks on the diffractograms were successfully identified and corresponded to the data from the reference card (JCPDS Card No. 19-0629). The diffractograms of magnetite MNPs powders of different sizes are almost indistinguishable from one another. Table 1 presents the crystallite sizes calculated from the most intense peak. Table 1. Crystallite sizes of FO MNPs. Sample Average MNPs diameter (according to TEM data), nm Average crystalline size (according to XRD data), nm FO1 12.7 ± 1.6 12.0 ± 1.9 FO2 25.9 ± 3.4 13.3 ± 1.8 FO3 47.7 ± 4.3 12.6 ± 1.4 The crystallite size for the FO1 sample was 12.0 ± 1.9, for FO2 – 13.3 ± 1.8 nm, for FO3 – 12.6 ± 1.4 nm. It can be noted that the crystallite sizes for particles of different sizes coincide within the margin of error and are approximately equal to the average diameter of FO1 MNPs. For larger particles, the crystallite size is smaller than their average diameter, which indicates that the particles have a polycrystalline structure. Fig. 6 and 7 show the diffractograms of the FO@BTO nanocomposite powder with different FO nanoparticle sizes before (Figure 6) and after (Figure 7) annealing. All peaks on the diffractograms were successfully identified and correspond to the data from reference cards (JCPDS Card No. 19-0629 for FO phase and JCPDS Card No. 81-2203 for BTO phase). The crystalline peaks on the diffractogram for annealed FO@BTO particles are better resolved and narrower. According to Table 2, an increase in crystallite size is observed in all samples for the BTO phase after annealing which may indicate growth of the crystalline structure following heat treatment. For example, in the case of FO1@BTO, the crystallite size BTO increases from 8.8 ± 1.6 to 11.4 ± 2.7 nm. In the case of FO2@BTO, the crystallite size of BTO increases from 9.1 ± 1.7 to 12.9 ± 3.5 nm. In the FO3@BTO sample, an increase in crystallite size is also observed, with BTO increasing from 8.4 ± 1.4 to 12.1 ± 3.1 nm. According to Tables 1 and 2, when coating FO nanoparticles with a BTO shell, no significant change in crystallite size occurs. The change in FO crystallite size (within the margin of error) after annealing occurred only in the FO3@BTO (from 12.8 ± 1.7 nm for not annealed to 17.0 ± 3.5 nm for annealed sample) sample with the largest core size (47.7 ± 4.3 nm) , which indicates recrystallization of such MNPs during annealing. Table 2. Crystallite sizes of composite components before and after annealing. Sample Core size, nm (TEM) FO crystallite size, nm (XRD) BTO crystallite size, nm (XRD) Before annealing After annealing Before annealing After annealing FO1@BTO 12.7 ± 1.6 12.8 ± 1.8 12.5 ± 1.6 8.8 ± 1.6 11.4 ± 2.7 FO2@BTO 25.9 ± 3.4 12.3 ± 1.6 14.9 ± 2.3 9.1 ± 1.7 12.9 ± 3.5 FO3@BTO 47.7 ± 4.3 12.8 ± 1.7 17.0 ± 3.5 8.4 ± 1.4 12.1 ± 3.1 According to Table 3, annealing leads to an increase in the volumetric content of the crystalline BTO phase in the sample. For FO1@BTO sample – from 63 ± 8 % to 71 ± 9 %, for FO2@BTO – from 65 ± 11 % to 82 ± 5 %, for FO3@BTO – from 61 ± 13 % to 82 ± 6 %, the following conclusions can be drawn: after annealing, impurity peaks disappear from the sample’s diffractogram, and the content of the crystalline BTO phase and the size of BTO crystallites increase. This can be explained by the formation reaction of BTO. As a result, after measurements, it can be concluded that FO@BTO nanocomposites with cores of various diameters were indeed obtained with almost no impurities. The content of the crystalline FO phase in the composite is in the range from 18 ± 6 % to 29 ± 9 % for annealed MENPs. Table 3. Crystalline properties of FO@BTO MENPs. Sample Core size, nm (TEM) Ratio of FO Crystalline Phase to BTO Crystalline Phase Before annealing After annealing FO1@BTO 12.7 ± 1.6 36% : 63% (±8%) 29% : 71% (±9%) FO2@BTO 25.9 ± 3.4 35% :65% (±11%) 18% : 82% (±5%) FO3@BTO 47.7 ± 4.3 39% : 61% (±13%) 18% : 82% (±6%) Magnetostrictive measurements Table 4 presents the data on the magnetostriction measurements of the samples. According to theoretical studies [34], in saturation fields, if there is no volume magnetostriction, λ l = -2λ T (λ l – coefficient of longitudinal magnetostriction, λ T – coefficient of transverse magnetostriction). We conducted measurements in fields stronger than the saturation fields for magnetite, as described in [34]. The values of the transverse magnetostriction coefficient at a magnetic field of 20 kOe are as follows: -4.2 ± 1.8 ppm for non-annealed FO1 MNPs, -4.5 ± 1.9 ppm for non-annealed FO2 MNPs, and -9.0 ± 3.3 ppm for non-annealed FO3 MNPs. The values of the longitudinal magnetostriction coefficient at a magnetic field of 10 kOe are as follows: 6.5 ± 2.9 ppm for non-annealed FO1 MNPs, 6.8 ± 1.7 ppm for non-annealed FO2 MNPs, and 14.6 ± 2.4 ppm for non-annealed FO3 MNPs. Table 4. Magnetostriction coefficients of FO MNPs. Sample MNPs size, nm λ T , ppm (H=20 kOe) λ l ,ppm (H=10 kOe) λ l + 2λ T , ppm FO1 12.7 ± 1.6 -4.2 ±1.8 6.5 ± 2.9 -1.9 ±3.9 FO2 25.9 ± 3.4 -4.5 ± 1.9 6.8 ± 1.7 -2.2 ± 3.2 FO2 47.7 ± 4.3 -9.0 ± 3.3 14.6 ±2.4 -3.4 ±5.2 From Table 4, it can be observed that, within the margin of error, the λ l = -2λ T ratio holds true: -1.9 ± 3.9 ppm for non-annealed FO1 MNPs, -2.2 ± 3.2 ppm for non-annealed FO2 MNPs, and -3.4 ± 2.2 ppm for non-annealed FO3 MNPs. It is important to note that the magnetostriction value for individual nanoparticles will be higher than the measured value for the compressed pellet because, during pressing, voids remain in the sample. These voids expand without deforming the strain gauge. Thus, the presence of magnetostriction in the investigated samples has been confirmed. However, further research should focus on measurements in high-frequency magnetic fields, allowing the transmission of a large number of pulses per second, as well as in lower amplitude fields, so that the sources of such fields can be of a size suitable for everyday applications. VSM measurements The magnetic measurement data of the samples are presented in Figures 8 and 9 and Tables 5 and 6. Table 5 shows the correlation between the coercive field and the magnetostrictive properties of the MNPs. The coercivity of the sample FO1 is 0.10 ± 0.05 Oe, with a longitudinal magnetostriction coefficient of -6.5 ppm. The FO2 sample has a coercivity of 2.00 ± 0.05 Oe, and a longitudinal magnetostriction coefficient of -6.8 ppm. The FO3 sample has a coercive force of 40.10 ± 0.05 Oe and a longitudinal magnetostriction coefficient of -14.6 ppm. Particles of the FO1 sample show superparamagnetic behavior (low values of coercivity and remanent magnetization: Hc = 0.10 ± 0.05 Oe, Mr = 0.20 ± 0.02 emu/g.), while particles with a diameter of 47.3 nm exhibit ferromagnetic (Hc = 40.10 ± 0.05 Oe, Mr = 10.90 ± 0.02 emu/g) behavior (Fig.8, Tab.1). Table 5. Magnetic properties of FO MNPs. Sample MNPs size, nm Нс, Ое Mr, emu/g Ms, emu/g λ l ,ppm (H=10 kOe) λ T , ppm (H=20 kOe) FO1 12.7 ± 1.6 0.10 ± 0.05 0.20 ± 0.02 59.9 ± 0.02 6.5 ± 2.9 -4.2 ± 1.8 FO2 25.9 ± 3.4 2.00 ± 0.05 0.50 ± 0.02 68.4 ± 0.02 6.8 ± 1.7 -4.5 ± 1.9 FO3 47.7 ± 4.3 40.10 ± 0.05 10.90 ± 0.02 72.1 ± 0.02 14.6 ± 2.4 -9.0 ± 3.3 Table 6. Magnetic properties of FO@BTO MENPs. Sample Annealing Core size, nm Нс, Ое Mr, emu/g Ms, emu/g Crystalline FO: Crystalline BTO FO1@BTO No 12.7 ± 1.6 9.60 ± 0.05 1.10 ± 0.02 25.1± 0.02 36% : 63% (±8%) FO1@BTO Yes 25.9 ± 3.4 No data No data No data 29% : 71% (±9%) FO2@BTO No 47.7 ± 4.3 17.10 ± 0.05 1.50 ± 0.02 20.4± 0.02 35% :65% (±11%) FO2@BTO Yes 12.7 ± 1.6 10.80 ± 0.05 0.70 ± 0.02 13.2± 0.02 18% : 82% (±5%) FO3@BTO No 25.9 ± 3.4 32.40 ± 0.05 1.90 ± 0.02 18.1± 0.02 39% : 61% (±13%) FO3@BTO Yes 47.7 ± 4.3 26.80 ± 0.05 1.20 ± 0.02 9.7± 0.02 18% : 82% (±6%) According to Tables 5 and 6 and Fig. 9, the FO@BTO samples show a significant contribution from the ferromagnetic properties of barium titanate nanoparticles [35, 36]. Upon further annealing, the reduction in coercive force, saturation magnetization, and remanent magnetization values in the FO@BTO samples is influenced by changes in the magnetic properties of barium titanate due to its recrystallization. Additionally, the decrease in saturation magnetization after the annealing can be explained by the oxidation of magnetite, which is the magnetic component of FO@BTO to maghemite [37, 38]. Probe microscopy measurements For AFM measurements, FO2@BTO particles with a core size of 25.9 ± 3.4 nm were selected. This sample was chosen due to the absence of impurities and because it exhibited the most well-defined “core-shell like” structure, despite demonstrating poorer magnetic properties compared to composites with larger core sizes. The measurements were conducted using the sample after annealing and milling. Measurements were conducted without a magnetic field and in a longitudinal magnetic field of H=2 kOe. Although no piezoelectric effect was detected on agglomerates of particles with a diameter of about 200 nm without the application of a magnetic field (Fig. 10 a, b, c), after applying a constant longitudinal magnetic field of H=2 kOe, the contrast in vertical amplitude and vertical phase of the piezoresponse changed (Fig. 10 d, e, f). On the basis of these plots, it can be said that with the background contrast unchanged, the piezoresponse phase changed by approximately 0.5 degrees when the magnetic field was applied. Qualitatively, it can be observed that the piezoresponse amplitude decreased, but drawing conclusions about the quantitative characteristics of the change in piezoresponse amplitude is challenging. Similar data were obtained from another group of particles of comparable diameter (Fig. 11). In this group of particles, a vertical piezoresponse was observed in the area containing the particle without the application of a magnetic field. When a magnetic field was applied, the piezoresponse amplitude decreased, and the phase increased by a value ranging from 0.2 to 0.5 degrees. To obtain quantitative data on the piezoresponse and magnetoelectric effect in the sample, refinement of the sample preparation and measurement protocols is necessary. It may be worth attempting measurements with a pre-polarized sample. Conclusions This work presents a comprehensive study of the magnetic, magnetostrictive, and structural properties of magnetoelectric nanocomposites that show promise for use in magnetically controlled neurostimulation. In this work, low-toxicity magnetite nanoparticles were selected as the magnetostrictive core of the magnetoelectric particles. Three groups of nanoparticles with average sizes of 12.7 (FO1), 25.9 (FO2), and 47.7 (FO3) nm were synthesized. According to XRD measurements, all particles have a polycrystalline structure. For each group of particles, the magnetostriction values of the samples were measured using strain gauges. The longitudinal magnetostriction coefficient of nanoparticles with average sizes of 12.7 (FO1), 25.9 (FO2), and 47.3 (FO3) nm was 6.5, 6.8, and 14.6 ppm, respectively. The resulting magnetoelectric composites were obtained by solvothermal crystallization of BaTiO 3 in medium containing pre-synthesized magnetic nanoparticles with subsequent annealing for 6 hours at a temperature of 700 °C and grinding in oleic acid media for 12 hours. Based on TEM images, composite sample with core size of 25.9 nm and the structure most closely resembling a core-shell type (FO2@BTO) was selected for magnetoelectric measurements. Magnetoelectric measurements were carried out using methods of piezoresponse force microscopy. On the selected sample, amplitude and phase images of the piezoresponse were obtained both without and under the application of a magnetic field with a strength of 2 kOe longitudinal to the sample surface. The study qualitatively demonstrated the change in amplitude and phase of the sample’s vertical piezoresponse when a magnetic field was applied, confirming the presence of the magnetoelectric effect. This fact, combined with usage of iron oxide core (instead of more widespread and toxic cobalt ferrite), makes the core-shell structured composite magnetoelectric nanoparticles promising for biomedical applications, including neurostimulation. References Allison, B.Z., Neuper, C. (2010). Could Anyone Use a BCI?. In: Tan, D., Nijholt, A. (eds) Brain-Computer Interfaces. Human-Computer Interaction Series. Springer, London. https://doi.org/10.1007/978-1-84996-272-8_3 G. Schalk, D. J. McFarland, T. Hinterberger, N. Birbaumer and J. R. 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FIU Electronic Theses and Dissertations. https://doi.org/10.25148/etd.FIDC004721 R. Abiri, S. Borhani, J. Kilmarx, C. Esterwood, Y. Jiang and X. Zhao, “A Usability Study of Low-Cost Wireless Brain-Computer Interface for Cursor Control Using Online Linear Model,” in IEEE Transactions on Human-Machine Systems , vol. 50, no. 4, pp. 287-297, Aug. 2020, doi: 10.1109/THMS.2020.2983848. Nizamov, T.R.; Amirov, A.A.; Kuznetsova, T.O.; Dorofievich, I.V.; Bordyuzhin, I.G.; Zhukov, D.G.; Ivanova, A.V.; Gabashvili, A.N.; Tabachkova, N.Y.; Tepanov, A.A.; et al. Synthesis and Functional Characterization of Co x Fe 3−x O 4 -BaTiO 3 Magnetoelectric Nanocomposites for Biomedical Applications. Nanomaterials 2023, 13, 811. Chaudhuri, A., & Mandal, K. (2015). Large magnetoelectric properties in CoFe2O4:BaTiO3 core–shell nanocomposites. Journal of Magnetism and Magnetic Materials, 377, 441–445 Khan, M., Kumari, M., Pawar, H., Dwivedi, U. K., Kurchania, R., & Rathore, D. (2021). Effect of concentration on sensing properties of CoFe2O4/BaTiO3 nanocomposites towards LPG. Applied Physics A, 127(9). Selvi, M. M., Manimuthu, P., Kumar, K. S., & Venkateswaran, C. (2014). Magnetodielectric properties of CoFe2O4–BaTiO3 core–shell nanocomposite. Journal of Magnetism and Magnetic Materials, 369, 155–161. Rasly, M., Afifi, M., Shalan, A. E., & Rashad, M. M. (2017). A quantitative model based on an experimental study for the magnetoelectric coupling at the interface of cobalt ferrite–barium titanate nanocomposites. Applied Physics A, 123(5). Gao, R., Xue, Y., Wang, Z., Chen, G., Fu, C., Deng, X., … Cai, W. (2020). Effect of particle size on magnetodielectric and magnetoelectric coupling effect of CoFe2O4@BaTiO3 composite fluids. Journal of Materials Rao, B. N., Kaviraj, P., Vaibavi, S. R., Kumar, A., Bajpai, S. K., & Arockiarajan, A. (2017). Investigation of magnetoelectric properties and biocompatibility of CoFe2O4 core-shell nanoparticles for biomedical applications. Journal of Applied Physics, 122(16), 164102-BaTiO3 Hathout A. S. et al. Synthesis and characterization of cobalt ferrites nanoparticles with cytotoxic and antimicrobial properties //Journal of Applied Pharmaceutical Science. – 2017. – Т. 7. – №. 1. – С. 086-092. Mmelesi O. K. et al. Cobalt ferrite nanoparticles and nanocomposites: Photocatalytic, antimicrobial activity and toxicity in water treatment //Materials Science in Semiconductor Processing. – 2021. – Т. 123. – С. 105523. Garanina, A.S.; Nikitin, A.A.; Abakumova, T.O.; Semkina, A.S.; Prelovskaya, A.O.; Naumenko, V.A.; Erofeev, A.S.; Gorelkin, P.V.; Majouga, A.G.; Abakumov, M.A.; et al. Cobalt Ferrite Nanoparticles for Tumor Therapy: Effective Heating versus Possible Toxicity. Nanomaterials 2022, 12 , 38. https://doi.org/10.3390/nano12010038 Zhang, D., & Du, Y. (2006). The biocompatibility study of Fe3O4 magnetic nanoparticles used in tumor hyperthermia. In 2006 1s t IEEE International Conference on Nano/Micro Engineered and Molecular Systems (pp. 1–4). IEEE. https://doi.org/10.1109/NEMS.2006.334497 Abakumov, M., Nizamov, T., Yanchen, L., Shchetinin, I., Savchenko, A., Zhukov, D., & Majouga, A. (2020). Versatile seed-mediated method of CoxFe3-xO4 nanoparticles synthesis in glycol media via thermal decomposition. Materials Letters, 128210. doi:10.1016/j.matlet.2020.128210 K.P. Belov, Magnitostriktsionniye yavleniya i ikh technicheskiye prilozheniya [Magnetostriction phenomena and their technical applications], Nauka, Moscow, 1987 (in Russian). Lihong Yang, Hongmei Qiu, Liqing Pan, Zhengang Guo, Mei Xu, Jinhua Yin, Xuedan Zhao, Magnetic properties of BaTiO3 and BaTi1−xMxO3 (M=Co, Fe) nanocrystals by hydrothermal method, Journal of Magnetism and Magnetic Materials,Volume 350, 2014, Pages 1-5, ISSN 0304-8853, https://doi.org/10.1016/j.jmmm.2013.09.036. Tolstykh, N.A., Korotkova, T.N., Jaafari, F.D. et al. Dielectric and Magnetic Properties of Nanocrystal Barium Titanate, Strontium Titanate, and a Blended Nanoсomposite Based on Them. Bull. Russ. Acad. Sci. Phys. 83, 1086–1090 (2019). https://doi.org/10.3103/S1062873819090272 Jafari, A., Farjami Shayesteh, S., Salouti, M., & Boustani, K. (2015). Effect of annealing temperature on magnetic phase transition in Fe3O4 nanoparticles. Journal of Magnetism and Magnetic Materials, 379, 305–312.doi:10.1016/j.jmmm.2014.12.050 El-Shater, R., Fakhry, F., Kawamura, G. et al. Impact annealing temperature process on oxidation state of iron ions and structural phase transition in magnetite nanoparticles.Indian J Phys 97, 127–139 (2023). https://doi.org/10.1007/s12648-022-02349-5 Additional Declarations No competing interests reported. Supplementary Files AppendixFile.docx Cite Share Download PDF Status: Published Journal Publication published 14 Apr, 2025 Read the published version in Journal of Nanoparticle Research → Version 1 posted Editorial decision: Revision requested 14 Nov, 2024 Editor assigned by journal 07 Nov, 2024 Submission checks completed at journal 04 Nov, 2024 First submitted to journal 04 Nov, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-5390395\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":378073697,\"identity\":\"7d14ec9b-0bb4-4bea-a0d0-646b265111e2\",\"order_by\":0,\"name\":\"D. A. 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Blue – FO1, orange – FO2, green – FO3.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"5.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5390395/v1/d7ec5e5c9a48905ca4a4d097.png\"},{\"id\":69282325,\"identity\":\"2ce02e66-39f5-480d-a5de-c40dc8b3c945\",\"added_by\":\"auto\",\"created_at\":\"2024-11-18 18:59:28\",\"extension\":\"png\",\"order_by\":6,\"title\":\"Figure 6\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":193031,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eDiffractograms of FO@BTO nanocomposite powders with cores of various sizes before annealing. 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On the left – in full scale, on the right – near the origin.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"8.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5390395/v1/070846865f0b7a42c662b662.png\"},{\"id\":69282197,\"identity\":\"83db490e-5ac0-4323-9b26-0fb2677d6a45\",\"added_by\":\"auto\",\"created_at\":\"2024-11-18 18:57:47\",\"extension\":\"png\",\"order_by\":9,\"title\":\"Figure 9\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":220538,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eHysteresis loops for FO@BTO nanocomposites in two different scales. On the left – in full scale, on the right – near the origin.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"9.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5390395/v1/f16815e1bfc4504098b30270.png\"},{\"id\":69282254,\"identity\":\"6a4f8048-c2a8-4503-b9ab-d0482127bf84\",\"added_by\":\"auto\",\"created_at\":\"2024-11-18 18:58:47\",\"extension\":\"png\",\"order_by\":10,\"title\":\"Figure 10\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":785029,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eTopography (a, d), vertical piezoresponse amplitude (b, e), and vertical piezoresponse phase (c, f) of the FO2@BTO after annealing and milling under the application of zero magnetic field (a, b, c) and longitudinal magnetic field of B=0.2Т(d, e, f).\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"10.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5390395/v1/39cb6c42da1327facd0d5dfb.png\"},{\"id\":69282373,\"identity\":\"822a63d6-3883-4957-9683-7c2bba9232cb\",\"added_by\":\"auto\",\"created_at\":\"2024-11-18 18:59:50\",\"extension\":\"png\",\"order_by\":11,\"title\":\"Figure 11\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":838405,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eTopography (a, d), vertical piezoresponse amplitude (b, e), and vertical piezoresponse phase (c, f) of the FO2@BTO sample after annealing and milling under the application of яero magnetic field (a, b, c) and longitudinal magnetic field of B=2 0.2 Т (d, e, f).\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"11.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5390395/v1/359c6c1585ee85106ffe007e.png\"},{\"id\":81050977,\"identity\":\"11ccde39-3347-4869-8b8c-f105f3c17b98\",\"added_by\":\"auto\",\"created_at\":\"2025-04-21 16:09:15\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":3856124,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5390395/v1/21db3f28-a4bc-49a0-91e1-53cb98a24965.pdf\"},{\"id\":69282208,\"identity\":\"e1c9f820-44f5-4a5c-846a-2cbc68008054\",\"added_by\":\"auto\",\"created_at\":\"2024-11-18 18:58:26\",\"extension\":\"docx\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":4068959,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"AppendixFile.docx\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5390395/v1/5314cb821eca004c0e205606.docx\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"\\u003cp\\u003eLocal magnetoelectric effect in Fe\\u003csub\\u003e3\\u003c/sub\\u003eO\\u003csub\\u003e4\\u003c/sub\\u003e-BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e nanocomposites\\u003c/p\\u003e\",\"fulltext\":[{\"header\":\"Introduction\",\"content\":\"\\u003cp\\u003eRecently, the development and use of brain-computer interfaces (BCIs) — systems for exchanging information between the human brain and electronic devices — has attracted significant attention from researchers [1-3]. Today, BCIs are actively being used to enhance the functionality of prosthetics, restore vision and hearing, regain lost motor abilities, and treat Parkinson's disease, epilepsy, and dystonia [4-6]. However, there are still several limitations that prevent the widespread and effective use of BCIs [7,8]. To fully realize the potential of these interfaces, several important steps must be taken. For broad and long-term use, it is necessary to achieve minimally invasive implantation procedures, biocompatibility of materials for implants, and the safety of stimulating effects [9]. The number of neural channels that the implanted device can access must be increased by several orders of magnitude [10]. Spatial resolution should be equal to or smaller than the diameter of small groups of neurons (i.e., on the micron scale), and temporal resolution should be faster or comparable to that of neurons in the native brain (i.e., response time of less than a millisecond) [11].\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eIn the context of the aforementioned methods and considering the shortcomings of each, the primary focus of researches is the development of compact and safe systems that enable non-invasive “deep” brain stimulation with the prospect of reading signals received from neurons. In this regard, the use of a magnetic field as an external stimulus and composite magnetic nanoparticles (MNPs) for local “deep” effects appears to be very promising and meets the specified conditions [12-14]. The literature describes various approaches MNPs for signal transmission to and recording from neurons. For example, magnetothermal: due to magnetic hyperthermia, the area around the nanoparticle is heated, which can affect the neuron [13, 15-18]. Magneto-mechanical deformation [19]: \\u0026nbsp;a potential effect arises from the rotation of magnetic cores with magnetic anisotropy under the influence of a low frequency magnetic field; the mechanical stress on neuron, caused by the rotation, can trigger a transmittance of electrical impulse to another neuron. Magnetostrictive: the use of MENPs (nanocomposites) with a multiferroic nature, with a magnetostrictive core and a piezoelectric shell, is proposed; a potential difference arises on the surface of piezoelectric particles under mechanical stress due to the magnetostriction of the cores when a magnetic field is applied; through the potential difference induced on the particle surface, it is possible to transmit an electrical impulse to the neuron or read it from the neuron [11, 20-24].\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eExactly the magnetostrictive approach to deforming the piezoelectric shell and creating a potential on the surface of the MENPs for transmitting information to neurons is considered as promising for neurostimulation in many recent studies. Most of these studies are focused on the properties of MENPs based on cobalt ferrite, which are known for their strong magnetic characteristics compared to other spinel ferrites [22-29]. However, concerns remain regarding the biocompatibility and toxicity of cobalt ferrite nanoparticles, as they are not fully understood [30-32]. To address this, the current work proposes the use of FO with lower toxicity as the magnetostrictive phase of MENPs and BTO as the piezoelectric phase. Study of the structural, crystalline, magnetic, magnetostrictive and ME properties of MENPs for the magnetostrictive approach is the focus of this research. The general idea of this paper is based on the development of method to observe the local piezoresponse in low-toxicity biocompatible MENPs, which are promising for neurostimulation tuning by remotely applied magnetic field as a result of ME coupling.\\u0026nbsp;\\u003c/p\\u003e\"},{\"header\":\"Materials and Methods\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eChemicals \\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eIron (III) acetylacetonate (Fe(acac)\\u003csub\\u003e3\\u003c/sub\\u003e); triethylene glycol, 99% (TEG); titanium (IV) isopropoxide, 97%; barium hydroxide octahydrate (II) (Ba(OH)\\u003csub\\u003e2\\u003c/sub\\u003e\\u0026bull;8H\\u003csub\\u003e2\\u003c/sub\\u003eO); 1-octadecene, \\u0026ge; 95%; oleic acid, \\u0026ge; 99% (Roth; Germany); ethyl acetate, \\u0026nbsp;\\u0026ge;99.5%; butanol-1, \\u0026ge;99.4%; ethanol, \\u0026ge; 95%, polyvinylpyrrolidone, 10 kDa (PVP), Pluronic F127, deionized water. All the used chemicals except oleic acid and distilled water were provided by Sigma-Aldrich, USA.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eSynthesis of the samples\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe MENPs of Fe\\u003csub\\u003e3\\u003c/sub\\u003eO\\u003csub\\u003e4\\u003c/sub\\u003e@BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e with core-shell like structure, consisted of magnetic core of FO and piezoelectric shell of BTO were synthesized using following stages: thermal decomposition method for core synthesis and solvothermal method for shell synthesis. For this purpose was used the protocol described elsewhere\\u0026nbsp;[22, \\u0026nbsp;33].\\u003c/p\\u003e\\n\\u003cp\\u003eAs a result of the synthesis, three groups of FO nanoparticles FO1, FO2, and FO3, with 3 different core sizes were obtained. The particles from each group were then coated with a BTO shell, resulting in three different samples for further magnetoelectric measurements: FO1@BTO, FO2@BTO, and FO3@BTO. The characterization of the obtained samples is presented in the following chapters. Some of the particles were immediately taken for measurements, the other part was first annealed in a muffle furnace for 5 hours at a temperature of 700 \\u0026deg;C. \\u0026nbsp;Sample FO2@BTO was grounded in a Retsch MM301 ball mill for 12 hours in 25 ml tungsten carbide bowls using one ball with a diameter of 15 mm and 20 balls with a diameter of 1 mm. To stabilize the particles, octadecene and oleic acid were added to them during grinding. The synthesis process will be detailed in Appendix A.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eCharacterization\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe morphology of the MENPs was studied using JEM-1400 transmission electron microscope (TEM) (JEOL; Japan) with an accelerating voltage 120 kV.\\u0026nbsp;TEM images show the structure of the nanoparticles. MNPs average size was determined using the ImageJ software. For this purpose, the sizes of 100 randomly selected particles from the image were measured, followed by the construction of size distribution histograms.\\u003c/p\\u003e\\n\\u003cp\\u003eStructure and phase analysis\\u0026nbsp;were performed using a STADI P powder diffractometer (STOE, Darmstadt, Germany).\\u0026nbsp;The measurements were carried out using an Image Plate detector. The sample preparation was as follows: the sample was ground in an agate mortar in ethanol media. After that, the sample was applied between two films using silicone grease. Both the film and the silicone grease are transparent to XRD radiation in the studied angular range. The film with the sample was then fixed in a cuvette. The X-ray diffraction analysis in the angular range of (20\\u0026ndash;100)\\u0026deg;\\u0026nbsp;at room temperature was conducted using the Rietveld method with the FullProf software with a step 0.002\\u0026deg;.\\u003c/p\\u003e\\n\\u003cp\\u003eTo study the magnetic properties of the investigated particles, their hysteresis magnetization loops were recorded. Magnetic measurements were carried out using Lakeshore 7407 VSM (Lake Shore Cryotronics, USA) at room temperature. The\\u0026nbsp;powdered samples\\u0026nbsp;were sealed in polyethylene capsules with approximate dimensions of 4x4x0.5 mm. The capsules were not laminated to prevent sample degradation, and for this reason, the particles could move during the measurements. The capsule was fixed to the holder using a Teflon tape. The magnetic field up to 16 kOe was applied in the plane of the capsule to minimize the influence of the demagnetizing field.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eThe local ME effect was studied using PFM technique with АСМ NTEGRA PRIMA commercial scanning probe microscope. For these measurements, commercial cantilevers HA_HR/W2C, NSG01/Pt, NSG01/TiN were utilized. The sample was suspended in ethanol and then applied to a conductive copper tape. Measurements were carried out both without and with the application of a magnetic field (H = 2 kOe). The magnetic field was applied parallel to the surface of the sample.\\u003c/p\\u003e\\n\\u003cp\\u003eMagnetostrictive measurements were conducted using self-designed experimental set-up based strain gauges measurements technique. The values of the longitudinal and transverse magnetostriction coefficients of FO nanoparticles were measured before MNPs annealing. The experimental setup and measurement methodology are described in detail in Appendix B.\\u003c/p\\u003e\"},{\"header\":\"Results and discussion\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eTEM measurements\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eAs a result of the synthesis, FO@BTO particles with cores of three different sizes (FO1 with average size D=12.7\\u0026plusmn;1.6 nm, FO2 with average size D=25.9\\u0026plusmn;3.4 nm, FO3 with average size D=47.7\\u0026plusmn;4.3 nm) were obtained (Fig. 1). In this figure, the polycrystalline structure of the obtained MNPs is clearly visible. Figure 2 shows the histograms of nanoparticle size distribution. Suspensions of particles of all sizes demonstrate colloidal stability in triethylene glycol (TEG) over an extended period. However, in the image of FO3 (Fig. 1 c), it can be seen that the MNPs have sufficient residual magnetization to align into chains in a less viscous medium, such as ethanol. Fig. 3 shows an image of the FO@BTO composite. In this image, one can see the BTO matrix, within which particles or clusters of FO nanoparticles are embedded. In such a structure, the magnetoelectric effect should be observed. However, due to the inhomogeneity of the obtained sample, the interaction between the magnetic (FO) and electrical (BTO) subsystems will vary in different areas of the sample. Therefore, in some regions of the sample, AFM measurements should show the presence of surface potential induced by the magnetic field, while in others, they should not.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eAlthough the FO3 MNPs demonstrate (as will be shown later) the best magnetic, including magnetostrictive, properties, they tend to clump into chains due to their high spontaneous magnetization (Fig. 1 c). This necessitates additional surface treatment of the particles before coating them with BTO to achieve a uniform coating of the magnetic core with the BTO shell. According to [22], during milling, the composite should break down into individual particles. In Fig. 4, it can be seen that after annealing and milling with stabilizers, the composite breaks down into smaller clusters of about several hundred nanometers in size.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eFor further measurements using probe methods, FO2@BTO sample was selected, as it demonstrates greater stability compared to larger MENPs and superior magnetic properties compared to smaller MENPs.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eXRD measurements\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eFigure 5 shows the diffractogram of magnetite MNPs powders of different sizes. All peaks on the diffractograms were successfully identified and corresponded to the data from the reference card (JCPDS Card No. 19-0629). The diffractograms of magnetite MNPs powders of different sizes are almost indistinguishable from one another. Table 1 presents the crystallite sizes calculated from the most intense peak. \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eTable 1. Crystallite sizes of FO MNPs.\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 33.2781%;\\\"\\u003e\\n \\u003cp\\u003eSample\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 33.2781%;\\\"\\u003e\\n \\u003cp\\u003eAverage MNPs diameter (according to TEM data), nm\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 33.4437%;\\\"\\u003e\\n \\u003cp\\u003eAverage crystalline size (according to XRD data), nm\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 33.2781%;\\\"\\u003e\\n \\u003cp\\u003eFO1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 33.2781%;\\\"\\u003e\\n \\u003cp\\u003e12.7\\u0026nbsp;\\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 33.4437%;\\\"\\u003e\\n \\u003cp\\u003e12.0 \\u0026plusmn; 1.9\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 33.2781%;\\\"\\u003e\\n \\u003cp\\u003eFO2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 33.2781%;\\\"\\u003e\\n \\u003cp\\u003e25.9\\u0026nbsp;\\u0026plusmn; 3.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 33.4437%;\\\"\\u003e\\n \\u003cp\\u003e13.3 \\u0026plusmn; 1.8\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 33.2781%;\\\"\\u003e\\n \\u003cp\\u003eFO3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 33.2781%;\\\"\\u003e\\n \\u003cp\\u003e47.7\\u0026nbsp;\\u0026plusmn; 4.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 33.4437%;\\\"\\u003e\\n \\u003cp\\u003e12.6 \\u0026plusmn; 1.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003eThe crystallite size for the FO1 sample was 12.0 \\u0026plusmn; 1.9, for FO2 \\u0026ndash; 13.3 \\u0026plusmn; 1.8 nm, for FO3 \\u0026ndash; 12.6 \\u0026plusmn; 1.4 nm. It can be noted that the crystallite sizes for particles of different sizes coincide within the margin of error and are approximately equal to the average diameter of FO1 MNPs. For larger particles, the crystallite size is smaller than their average diameter, which indicates that the particles have a polycrystalline structure.\\u003c/p\\u003e\\n\\u003cp\\u003eFig. 6 and 7 show the diffractograms of the FO@BTO nanocomposite powder with different FO nanoparticle sizes before (Figure 6) and after (Figure 7) annealing.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eAll peaks on the diffractograms were successfully identified and correspond to the data from reference cards (JCPDS Card No. 19-0629 for FO phase and JCPDS Card No. 81-2203 for BTO phase). The crystalline peaks on the diffractogram for annealed FO@BTO particles are better resolved and narrower.\\u003c/p\\u003e\\n\\u003cp\\u003eAccording to Table 2, an increase in crystallite size is observed in all samples for the BTO phase after annealing which may indicate growth of the crystalline structure following heat treatment. For example, in the case\\u0026nbsp;of FO1@BTO, the crystallite size BTO increases from 8.8 \\u003cstrong\\u003e\\u0026plusmn; 1.6\\u003c/strong\\u003e\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003eto 11.4 \\u003cstrong\\u003e\\u0026plusmn; 2.7\\u003c/strong\\u003e\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003enm. In the case of FO2@BTO, the crystallite size of BTO increases from 9.1 \\u003cstrong\\u003e\\u0026plusmn; 1.7\\u003c/strong\\u003e\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003eto 12.9 \\u003cstrong\\u003e\\u0026plusmn; 3.5\\u003c/strong\\u003e\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003enm. In the FO3@BTO sample, an increase in crystallite size is also observed, with BTO increasing from 8.4 \\u003cstrong\\u003e\\u0026plusmn; 1.4\\u003c/strong\\u003e\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003eto 12.1 \\u003cstrong\\u003e\\u0026plusmn; 3.1\\u003c/strong\\u003e\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003enm. According to Tables 1 and 2, when coating FO nanoparticles with a BTO shell, no significant change in crystallite size occurs. The change in FO crystallite size (within the margin of error) after annealing occurred only in the FO3@BTO (from 12.8 \\u003cstrong\\u003e\\u0026plusmn; 1.7 nm for not annealed to 17.0 \\u0026plusmn; 3.5 nm for annealed sample)\\u0026nbsp;\\u003c/strong\\u003esample with the largest core size (47.7 \\u003cstrong\\u003e\\u0026plusmn; 4.3 nm)\\u003c/strong\\u003e, which indicates recrystallization of such MNPs during annealing.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 2. Crystallite sizes of composite components before and after annealing.\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"604\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd rowspan=\\\"2\\\" style=\\\"width: 113px;\\\"\\u003e\\n \\u003cp\\u003eSample\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd rowspan=\\\"2\\\" style=\\\"width: 98px;\\\"\\u003e\\n \\u003cp\\u003eCore size, nm\\u003c/p\\u003e\\n \\u003cp\\u003e(TEM)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd colspan=\\\"2\\\" style=\\\"width: 195px;\\\"\\u003e\\n \\u003cp\\u003eFO crystallite size, nm (XRD)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd colspan=\\\"2\\\" style=\\\"width: 198px;\\\"\\u003e\\n \\u003cp\\u003eBTO crystallite size, nm (XRD)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 98px;\\\"\\u003e\\n \\u003cp\\u003eBefore annealing\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 97px;\\\"\\u003e\\n \\u003cp\\u003eAfter annealing\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 94px;\\\"\\u003e\\n \\u003cp\\u003eBefore annealing\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 104px;\\\"\\u003e\\n \\u003cp\\u003eAfter annealing\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 113px;\\\"\\u003e\\n \\u003cp\\u003eFO1@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 98px;\\\"\\u003e\\n \\u003cp\\u003e12.7 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 98px;\\\"\\u003e\\n \\u003cp\\u003e12.8 \\u0026plusmn; 1.8\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 97px;\\\"\\u003e\\n \\u003cp\\u003e12.5 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 94px;\\\"\\u003e\\n \\u003cp\\u003e8.8 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 104px;\\\"\\u003e\\n \\u003cp\\u003e11.4 \\u0026plusmn; 2.7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 113px;\\\"\\u003e\\n \\u003cp\\u003eFO2@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 98px;\\\"\\u003e\\n \\u003cp\\u003e25.9 \\u0026plusmn; 3.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 98px;\\\"\\u003e\\n \\u003cp\\u003e12.3 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 97px;\\\"\\u003e\\n \\u003cp\\u003e14.9 \\u0026plusmn; 2.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 94px;\\\"\\u003e\\n \\u003cp\\u003e9.1 \\u0026plusmn; 1.7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 104px;\\\"\\u003e\\n \\u003cp\\u003e12.9 \\u0026plusmn; 3.5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 113px;\\\"\\u003e\\n \\u003cp\\u003eFO3@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 98px;\\\"\\u003e\\n \\u003cp\\u003e47.7 \\u0026plusmn; 4.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 98px;\\\"\\u003e\\n \\u003cp\\u003e12.8 \\u0026plusmn; 1.7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 97px;\\\"\\u003e\\n \\u003cp\\u003e17.0 \\u0026plusmn; 3.5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 94px;\\\"\\u003e\\n \\u003cp\\u003e8.4 \\u0026plusmn; 1.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 104px;\\\"\\u003e\\n \\u003cp\\u003e12.1 \\u0026plusmn; 3.1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003eAccording to Table 3, annealing leads to an increase in the volumetric content of the crystalline BTO phase in the sample. For FO1@BTO sample \\u0026ndash; from 63 \\u003cstrong\\u003e\\u0026plusmn; 8 % to 71 \\u0026plusmn; 9 %, for FO2@BTO \\u0026ndash; from 65 \\u0026plusmn; 11 % to 82 \\u0026plusmn; 5 %, for FO3@BTO \\u0026ndash; from 61 \\u0026plusmn; 13 % to 82 \\u0026plusmn; 6 %,\\u0026nbsp;\\u003c/strong\\u003ethe following conclusions can be drawn: after annealing, impurity peaks disappear from the sample\\u0026rsquo;s diffractogram, and the content of the crystalline BTO phase and the size of BTO crystallites increase. This can be explained by the formation reaction of BTO. As a result, after measurements, it can be concluded that FO@BTO nanocomposites with cores of various diameters were indeed obtained with almost no impurities. The content of the crystalline FO phase in the composite is in the range from 18 \\u003cstrong\\u003e\\u0026plusmn; 6 %\\u0026nbsp;\\u003c/strong\\u003eto 29 \\u003cstrong\\u003e\\u0026plusmn; 9 %\\u0026nbsp;\\u003c/strong\\u003efor annealed MENPs.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 3. Crystalline properties of FO@BTO MENPs.\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"604\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd rowspan=\\\"2\\\" style=\\\"width: 132px;\\\"\\u003e\\n \\u003cp\\u003eSample\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd rowspan=\\\"2\\\" style=\\\"width: 113px;\\\"\\u003e\\n \\u003cp\\u003eCore size, nm\\u003c/p\\u003e\\n \\u003cp\\u003e(TEM)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd colspan=\\\"2\\\" valign=\\\"bottom\\\" style=\\\"width: 359px;\\\"\\u003e\\n \\u003cp\\u003eRatio of FO Crystalline Phase to BTO Crystalline Phase\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 180px;\\\"\\u003e\\n \\u003cp\\u003eBefore annealing\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 180px;\\\"\\u003e\\n \\u003cp\\u003eAfter annealing\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 132px;\\\"\\u003e\\n \\u003cp\\u003eFO1@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 113px;\\\"\\u003e\\n \\u003cp\\u003e12.7 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 180px;\\\"\\u003e\\n \\u003cp\\u003e36% :\\u0026nbsp;63%\\u0026nbsp;(\\u0026plusmn;8%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 180px;\\\"\\u003e\\n \\u003cp\\u003e29% : 71%\\u0026nbsp;(\\u0026plusmn;9%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 132px;\\\"\\u003e\\n \\u003cp\\u003eFO2@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 113px;\\\"\\u003e\\n \\u003cp\\u003e25.9 \\u0026plusmn; 3.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 180px;\\\"\\u003e\\n \\u003cp\\u003e35% :65%\\u0026nbsp;(\\u0026plusmn;11%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 180px;\\\"\\u003e\\n \\u003cp\\u003e18% : 82%\\u0026nbsp;(\\u0026plusmn;5%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 132px;\\\"\\u003e\\n \\u003cp\\u003eFO3@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 113px;\\\"\\u003e\\n \\u003cp\\u003e47.7 \\u0026plusmn; 4.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 180px;\\\"\\u003e\\n \\u003cp\\u003e39% :\\u0026nbsp;61%\\u0026nbsp;(\\u0026plusmn;13%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 180px;\\\"\\u003e\\n \\u003cp\\u003e18% : 82%\\u0026nbsp;(\\u0026plusmn;6%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eMagnetostrictive measurements\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eTable 4 presents the data on the magnetostriction measurements of the samples. According to theoretical studies [34], in saturation fields, if there is no volume magnetostriction,\\u0026nbsp;\\u0026lambda;\\u003csub\\u003el\\u003c/sub\\u003e = -2\\u0026lambda;\\u003csub\\u003eT\\u003c/sub\\u003e (\\u0026lambda;\\u003csub\\u003el\\u003c/sub\\u003e \\u0026ndash; coefficient of longitudinal magnetostriction, \\u0026lambda;\\u003csub\\u003eT\\u003c/sub\\u003e \\u0026ndash; coefficient of transverse magnetostriction). We conducted measurements in fields stronger than the saturation fields for magnetite, as described in [34]. The values of the transverse magnetostriction coefficient at a magnetic field of 20 kOe are as follows: -4.2 \\u0026plusmn; 1.8 ppm for non-annealed FO1 MNPs, -4.5 \\u0026plusmn; 1.9 ppm for non-annealed FO2 MNPs, and -9.0 \\u0026plusmn; 3.3 ppm for non-annealed FO3 MNPs. The values of the longitudinal magnetostriction coefficient at a magnetic field of 10 kOe are as follows: 6.5 \\u0026plusmn; 2.9 ppm for non-annealed FO1 MNPs, 6.8 \\u0026plusmn; 1.7 ppm for non-annealed FO2 MNPs, and 14.6 \\u0026plusmn; 2.4 ppm for non-annealed FO3 MNPs.\\u003c/p\\u003e\\n\\u003cp\\u003eTable 4. Magnetostriction coefficients of FO MNPs.\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"94%\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003eSample\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003eMNPs size, nm\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e\\u0026lambda;\\u003csub\\u003eT\\u003c/sub\\u003e, ppm (H=20\\u0026nbsp;kOe)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e\\u0026lambda;\\u003csub\\u003el\\u003c/sub\\u003e,ppm (H=10\\u0026nbsp;kOe)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e\\u0026lambda;\\u003csub\\u003el\\u0026nbsp;\\u003c/sub\\u003e+ 2\\u0026lambda;\\u003csub\\u003eT\\u003c/sub\\u003e, ppm\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003eFO1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e12.7 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e-4.2\\u0026nbsp;\\u0026plusmn;1.8\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e6.5 \\u0026plusmn; 2.9\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e-1.9 \\u0026plusmn;3.9\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003eFO2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e25.9 \\u0026plusmn; 3.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e-4.5\\u0026nbsp;\\u0026plusmn; 1.9\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e6.8 \\u0026plusmn; 1.7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e-2.2 \\u0026plusmn;\\u0026nbsp;3.2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003eFO2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e47.7 \\u0026plusmn; 4.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e-9.0\\u0026nbsp;\\u0026plusmn; 3.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e14.6 \\u0026plusmn;2.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 20%;\\\"\\u003e\\n \\u003cp\\u003e-3.4 \\u0026plusmn;5.2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003eFrom Table 4, it can be observed that, within the margin of error, the\\u0026nbsp;\\u0026lambda;\\u003csub\\u003el\\u003c/sub\\u003e = -2\\u0026lambda;\\u003csub\\u003eT\\u003c/sub\\u003e ratio holds true: -1.9 \\u0026plusmn; 3.9 ppm for non-annealed FO1 MNPs, -2.2 \\u0026plusmn; 3.2 ppm for non-annealed FO2 MNPs, and -3.4 \\u0026plusmn; 2.2 ppm for non-annealed FO3 MNPs. It is important to note that the magnetostriction value for individual nanoparticles will be higher than the measured value for the compressed pellet because, during pressing, voids remain in the sample. These voids expand without deforming the strain gauge. Thus, the presence of magnetostriction in the investigated samples has been confirmed. However, further research should focus on measurements in high-frequency magnetic fields, allowing the transmission of a large number of pulses per second, as well as in lower amplitude fields, so that the sources of such fields can be of a size suitable for everyday applications.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eVSM measurements\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe magnetic measurement data of the samples are presented in Figures 8 and 9 and Tables 5 and 6. Table 5 shows the correlation between the coercive field and the magnetostrictive properties of the MNPs. The coercivity of the sample FO1 is 0.10 \\u0026plusmn; 0.05 Oe, with a longitudinal magnetostriction coefficient of -6.5 ppm. The FO2 sample has a coercivity of 2.00 \\u0026plusmn; 0.05 Oe, and a longitudinal magnetostriction coefficient of -6.8 ppm. The FO3 sample has a coercive force of 40.10 \\u0026plusmn; 0.05 Oe and a longitudinal magnetostriction coefficient of -14.6 ppm. Particles of the FO1 sample show superparamagnetic behavior (low values of coercivity and remanent magnetization: Hc = 0.10 \\u0026plusmn; 0.05 Oe, Mr = 0.20 \\u0026plusmn; 0.02 emu/g.), while particles with a diameter of 47.3 nm exhibit ferromagnetic (Hc = 40.10 \\u0026plusmn; 0.05 Oe, Mr = 10.90 \\u0026plusmn; 0.02 emu/g) behavior (Fig.8, Tab.1).\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eTable 5. Magnetic properties of FO MNPs.\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"604\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 15.5629%;\\\"\\u003e\\n \\u003cp\\u003eSample\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003eMNPs size, nm\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003eНс, Ое\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003eMr, emu/g\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003eMs, emu/g\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e\\u0026lambda;\\u003csub\\u003el\\u003c/sub\\u003e,ppm (H=10\\u0026nbsp;kOe)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e\\u0026lambda;\\u003csub\\u003eT\\u003c/sub\\u003e, ppm (H=20\\u0026nbsp;kOe)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 15.5629%;\\\"\\u003e\\n \\u003cp\\u003eFO1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e12.7 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e0.10\\u0026nbsp;\\u0026plusmn; 0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e0.20\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e59.9\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e6.5\\u0026nbsp;\\u0026plusmn; 2.9\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e-4.2\\u0026nbsp;\\u0026plusmn; 1.8\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 15.5629%;\\\"\\u003e\\n \\u003cp\\u003eFO2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e25.9 \\u0026plusmn; 3.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e2.00\\u0026nbsp;\\u0026plusmn; 0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e0.50\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e68.4\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e6.8\\u0026nbsp;\\u0026plusmn; 1.7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e-4.5\\u0026nbsp;\\u0026plusmn; 1.9\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 15.5629%;\\\"\\u003e\\n \\u003cp\\u003eFO3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e47.7 \\u0026plusmn; 4.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e40.10\\u0026nbsp;\\u0026plusmn; 0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e10.90\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e72.1\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e14.6\\u0026nbsp;\\u0026plusmn; 2.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.0728%;\\\"\\u003e\\n \\u003cp\\u003e-9.0 \\u0026plusmn; 3.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003eTable 6. Magnetic properties of FO@BTO MENPs.\\u003c/p\\u003e\\n\\u003ctable border=\\\"1\\\" cellspacing=\\\"0\\\" cellpadding=\\\"0\\\" width=\\\"604\\\"\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 16.0066%;\\\"\\u003e\\n \\u003cp\\u003eSample\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.1914%;\\\"\\u003e\\n \\u003cp\\u003eAnnealing\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 11.8812%;\\\"\\u003e\\n \\u003cp\\u003eCore size, nm\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.1815%;\\\"\\u003e\\n \\u003cp\\u003eНс, Ое\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003eMr, emu/g\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003eMs, emu/g\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.3465%;\\\"\\u003e\\n \\u003cp\\u003eCrystalline FO: Crystalline BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 16.0066%;\\\"\\u003e\\n \\u003cp\\u003eFO1@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.1914%;\\\"\\u003e\\n \\u003cp\\u003eNo\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 11.8812%;\\\"\\u003e\\n \\u003cp\\u003e12.7 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.1815%;\\\"\\u003e\\n \\u003cp\\u003e9.60\\u0026nbsp;\\u0026plusmn; 0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e1.10\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e25.1\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.3465%;\\\"\\u003e\\n \\u003cp\\u003e36% :\\u0026nbsp;63%\\u0026nbsp;(\\u0026plusmn;8%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 16.0066%;\\\"\\u003e\\n \\u003cp\\u003eFO1@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.1914%;\\\"\\u003e\\n \\u003cp\\u003eYes\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 11.8812%;\\\"\\u003e\\n \\u003cp\\u003e25.9 \\u0026plusmn; 3.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.1815%;\\\"\\u003e\\n \\u003cp\\u003eNo data\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003eNo data\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003eNo data\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.3465%;\\\"\\u003e\\n \\u003cp\\u003e29% : 71%\\u0026nbsp;(\\u0026plusmn;9%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 16.0066%;\\\"\\u003e\\n \\u003cp\\u003eFO2@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.1914%;\\\"\\u003e\\n \\u003cp\\u003eNo\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 11.8812%;\\\"\\u003e\\n \\u003cp\\u003e47.7 \\u0026plusmn; 4.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.1815%;\\\"\\u003e\\n \\u003cp\\u003e17.10\\u0026nbsp;\\u0026plusmn; 0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e1.50\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e20.4\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.3465%;\\\"\\u003e\\n \\u003cp\\u003e35% :65%\\u0026nbsp;(\\u0026plusmn;11%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 16.0066%;\\\"\\u003e\\n \\u003cp\\u003eFO2@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.1914%;\\\"\\u003e\\n \\u003cp\\u003eYes\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 11.8812%;\\\"\\u003e\\n \\u003cp\\u003e12.7 \\u0026plusmn; 1.6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.1815%;\\\"\\u003e\\n \\u003cp\\u003e10.80\\u0026nbsp;\\u0026plusmn; 0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e0.70\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e13.2\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.3465%;\\\"\\u003e\\n \\u003cp\\u003e18% : 82%\\u0026nbsp;(\\u0026plusmn;5%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 16.0066%;\\\"\\u003e\\n \\u003cp\\u003eFO3@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.1914%;\\\"\\u003e\\n \\u003cp\\u003eNo\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 11.8812%;\\\"\\u003e\\n \\u003cp\\u003e25.9 \\u0026plusmn; 3.4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.1815%;\\\"\\u003e\\n \\u003cp\\u003e32.40\\u0026nbsp;\\u0026plusmn; 0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e1.90\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e18.1\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.3465%;\\\"\\u003e\\n \\u003cp\\u003e39% :\\u0026nbsp;61%\\u0026nbsp;(\\u0026plusmn;13%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd style=\\\"width: 16.0066%;\\\"\\u003e\\n \\u003cp\\u003eFO3@BTO\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 14.1914%;\\\"\\u003e\\n \\u003cp\\u003eYes\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 11.8812%;\\\"\\u003e\\n \\u003cp\\u003e47.7 \\u0026plusmn; 4.3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.1815%;\\\"\\u003e\\n \\u003cp\\u003e26.80\\u0026nbsp;\\u0026plusmn; 0.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e1.20\\u0026nbsp;\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 13.6964%;\\\"\\u003e\\n \\u003cp\\u003e9.7\\u0026plusmn; 0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd style=\\\"width: 15.3465%;\\\"\\u003e\\n \\u003cp\\u003e18% : 82% (\\u0026plusmn;6%)\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003cp\\u003eAccording to Tables 5 and 6 and Fig. 9, the FO@BTO samples show a significant contribution from the ferromagnetic properties of barium titanate nanoparticles [35, 36]. Upon further annealing, the reduction in coercive force, saturation magnetization, and remanent magnetization values in the FO@BTO samples is influenced by changes in the magnetic properties of barium titanate due to its recrystallization. Additionally, the decrease in saturation magnetization after the annealing can be explained by the oxidation of magnetite, which is the magnetic component of FO@BTO to maghemite [37, 38].\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eProbe microscopy measurements\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eFor AFM measurements, FO2@BTO particles with a core size of 25.9 \\u0026plusmn; 3.4 nm were selected. This sample was chosen due to the absence of impurities and because it exhibited the most well-defined \\u0026ldquo;core-shell like\\u0026rdquo; structure, despite demonstrating poorer magnetic properties compared to composites with larger core sizes. The measurements were conducted using the sample after annealing and milling. Measurements were conducted without a magnetic field and in a longitudinal magnetic field of H=2 kOe. Although no piezoelectric effect was detected on agglomerates of particles with a diameter of about 200 nm without the application of a magnetic field (Fig. 10 a, b, c), after applying a constant longitudinal magnetic field of H=2 kOe, the contrast in vertical amplitude and vertical phase of the piezoresponse changed (Fig. 10 d, e, f).\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eOn the basis of these plots, it can be said that with the background contrast unchanged, the piezoresponse phase changed by approximately 0.5 degrees when the magnetic field was applied. Qualitatively, it can be observed that the piezoresponse amplitude decreased, but drawing conclusions about the quantitative characteristics of the change in piezoresponse amplitude is challenging. Similar data were obtained from another group of particles of comparable diameter (Fig. 11). In this group of particles, a vertical piezoresponse was observed in the area containing the particle without the application of a magnetic field. When a magnetic field was applied, the piezoresponse amplitude decreased, and the phase increased by a value ranging from 0.2 to 0.5 degrees.\\u003c/p\\u003e\\n\\u003cp\\u003eTo obtain quantitative data on the piezoresponse and magnetoelectric effect in the sample, refinement of the sample preparation and measurement protocols is necessary. It may be worth attempting measurements with a pre-polarized sample.\\u003c/p\\u003e\"},{\"header\":\"Conclusions\",\"content\":\"\\u003cp\\u003eThis work presents a comprehensive study of the magnetic, magnetostrictive, and structural properties of magnetoelectric nanocomposites that show promise for use in magnetically controlled neurostimulation. \\u0026nbsp;In this work, low-toxicity magnetite nanoparticles were selected as the magnetostrictive core of the magnetoelectric particles. Three groups of nanoparticles with average sizes of 12.7 (FO1), 25.9 (FO2), and 47.7 (FO3) nm were synthesized. According to XRD measurements, all particles have a polycrystalline structure. For each group of particles, the magnetostriction values of the samples were measured using strain gauges. The longitudinal magnetostriction coefficient of nanoparticles with average sizes of 12.7 (FO1), 25.9 (FO2), and 47.3 (FO3) nm was 6.5, 6.8, and 14.6 ppm, respectively. \\u0026nbsp; The resulting magnetoelectric composites were obtained by solvothermal crystallization of BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e in medium containing pre-synthesized magnetic nanoparticles with subsequent annealing for 6 hours at a temperature of 700 \\u0026deg;C and grinding in oleic acid media for 12 hours. Based on TEM images, composite sample with core size of 25.9 nm and the structure most closely resembling a core-shell type (FO2@BTO) was selected for magnetoelectric measurements. Magnetoelectric measurements were carried out using methods of piezoresponse force microscopy. On the selected sample, amplitude and phase images of the piezoresponse were obtained both without and under the application of a magnetic field with a strength of 2 kOe longitudinal to the sample surface. The study qualitatively demonstrated the change in amplitude and phase of the sample\\u0026rsquo;s vertical piezoresponse when a magnetic field was applied, confirming the presence of the magnetoelectric effect. This fact, combined with usage of iron oxide core (instead of more widespread and toxic cobalt ferrite), makes the core-shell structured composite magnetoelectric nanoparticles promising for biomedical applications, including neurostimulation.\\u0026nbsp;\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\n\\u003cli\\u003eAllison, B.Z., Neuper, C. (2010). Could Anyone Use a BCI?. In: Tan, D., Nijholt, A. (eds) Brain-Computer Interfaces. Human-Computer Interaction Series. Springer, London. https://doi.org/10.1007/978-1-84996-272-8_3\\u003c/li\\u003e\\n\\u003cli\\u003eG. Schalk, D. J. McFarland, T. Hinterberger, N. Birbaumer and J. R. Wolpaw,\\u0026ldquo;\\u0026quot;BCI2000: a general-purpose brain-computer interface (BCI) system\\u0026rdquo;\\u0026quot; in \\u003cem\\u003eIEEE Transactions on Biomedical Engineering\\u003c/em\\u003e, vol. 51, no. 6, pp. 1034-1043, June 2004, doi: 10.1109/TBME.2004.827072.\\u003c/li\\u003e\\n\\u003cli\\u003eYogesh Kumar, Jitender Kumar, Poonam Sheoran, Integration of cloud computing in BCI: A review, Biomedical Signal Processing and Control, Volume 87, Part A, 2024, 105548, ISSN 1746-8094, https://doi.org/10.1016/j.bspc.2023.105548.\\u003c/li\\u003e\\n\\u003cli\\u003eWeiland, J. D., Cho, A. K., \\u0026amp; Humayun, M. S. (2011). Retinal prostheses: Current clinical results and future needs. \\u003cem\\u003eOphthalmology, 118\\u003c/em\\u003e(11), 2227\\u0026ndash;2237. https://doi.org/10.1016/j.ophtha.2011.07.047\\u003c/li\\u003e\\n\\u003cli\\u003eKringelbach, M., Jenkinson, N., \\u0026amp; Owen, S. (2007). Translational principles of deep brain stimulation. Nature Reviews Neuroscience, 8, 623 635. https://doi.org/10.1038/nrn2196\\u003c/li\\u003e\\n\\u003cli\\u003eAmon, A., \\u0026amp; Alesch, F. (2017). Systems for deep brain stimulation: Review of technical features. \\u003cem\\u003eJournal of Neural Transmission, 124\\u003c/em\\u003e(9), 1083\\u0026ndash;1091. https://doi.org/10.1007/s00702-017-1712-0\\u003c/li\\u003e\\n\\u003cli\\u003eChoi, W.-S.; Yeom, H.-G. Studies to Overcome Brain\\u0026ndash;Computer Interface Challenges. \\u003cem\\u003eAppl. Sci.\\u003c/em\\u003e 2022, \\u003cem\\u003e12\\u003c/em\\u003e, 2598. https://doi.org/10.3390/app12052598\\u003c/li\\u003e\\n\\u003cli\\u003eV\\u0026auml;rbu, K.; Muhammad, N.; Muhammad, Y. Past, Present, and Future of EEG-Based BCI Applications. \\u003cem\\u003eSensors\\u003c/em\\u003e 2022, \\u003cem\\u003e22\\u003c/em\\u003e, 3331. https://doi.org/10.3390/s22093331\\u003c/li\\u003e\\n\\u003cli\\u003eBrezovich, I. A. (1988). Low frequency hyperthermia: Capacitive and ferromagnetic thermoseed methods. \\u003cem\\u003eMedical Physics Monograph, 16\\u003c/em\\u003e, 82\\u0026ndash;111.\\u003c/li\\u003e\\n\\u003cli\\u003eWonsuk Choi \\u003cem\\u003eet al\\u003c/em\\u003e 2024 \\u003cem\\u003eJ. Neural Eng.\\u003c/em\\u003e 21 026004 \\u003cstrong\\u003eDOI\\u003c/strong\\u003e 10.1088/1741-2552/ad2d31\\u003c/li\\u003e\\n\\u003cli\\u003eWeinberg, I. N., Mair, L. O., Jafari, S., Algarin, J., Baviera, J. M. B., Baker-McKee, J., \\u0026hellip; Fricke, S. (2018). Image-guided placement of magnetic neuroparticles as a potential high-resolution brain-machine interface.\\u003c/li\\u003e\\n\\u003cli\\u003eHescham S. A. et al. Magnetothermal nanoparticle technology alleviates parkinsonian-like symptoms in mice //Nature communications. \\u0026ndash; 2021. \\u0026ndash; Т. 12. \\u0026ndash; №. 1. \\u0026ndash; С. 5569.\\u003c/li\\u003e\\n\\u003cli\\u003eKhanal, C. M. (2016). 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Effect of annealing temperature on magnetic phase transition in Fe3O4 nanoparticles. Journal of Magnetism and Magnetic Materials, 379, 305\\u0026ndash;312.doi:10.1016/j.jmmm.2014.12.050\\u003c/li\\u003e\\n\\u003cli\\u003eEl-Shater, R., Fakhry, F., Kawamura, G. et al. Impact annealing temperature process on oxidation state of iron ions and structural phase transition in magnetite nanoparticles.Indian J Phys 97, 127\\u0026ndash;139 (2023). https://doi.org/10.1007/s12648-022-02349-5\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"journal-of-nanoparticle-research\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"nano\",\"sideBox\":\"Learn more about [Journal of Nanoparticle Research](http://link.springer.com/journal/11051)\",\"snPcode\":\"11051\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11051/3\",\"title\":\"Journal of Nanoparticle Research\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"magnetoelectric effect, magnetic nanoparticles, magnetoelectric nanoparticles, multiferroic nanocomposites, iron oxide, piezoresponse force microscopy, magnetostriction.\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-5390395/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-5390395/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"Magnetoelectric nanoparticles (MENPs) are emerging as potential nanomaterials for a wide range of biomedical applications. Recently, many studies have been devoted to investigating the properties of MENPs based on cobalt ferrite. The outstanding magnetic properties of cobalt ferrite nanoparticles, such as higher values of coercive force and magnetostriction coefficient compared to other metal ferrites of spinel structures are well known. However, the biocompatibility and toxicity of cobalt ferrite nanoparticles are still a matter of debate and not fully studied. Therefore, design of MENPs with magnetic core having low toxicity is still a challenging task. Thus, we proposed to use iron oxide nanoparticles (FO) instead of cobalt ferrite as a less toxic alternative. This work represents a comprehensive study of the structural, crystalline, magnetic, and magnetoelectric (ME) properties of synthesized MENPs based on FO and barium titanate (BTO), where FO and BTO provide magnetostrictive and piezoelectric functionalities, respectively. The synthesis of FO of three sizes (12.7, 25.9, 47.7 nm) was carried out, after which the resulting nanoparticles were coated with BTO phase. Samples of all series were characterized by the methods of transmission electron microscopy (TEM), vibrating-sample magnetometry (VSM), X-ray diffraction (XRD) analysis. The longitudinal magnetostriction coefficient was found to be 6.5 ppm for FO with a diameter of 12.7 nm, 6.8 ppm with a diameter of 25.9 nm, and 14.6 ppm with a diameter of 47.7 nm. Piezoresponse force microscopy measurements qualitatively showed a change in the amplitude and phase of the piezoelectric response of MENPs when a magnetic field is applied to the sample.\",\"manuscriptTitle\":\"Local magnetoelectric effect in Fe3O4-BaTiO3 nanocomposites\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2024-11-18 17:38:59\",\"doi\":\"10.21203/rs.3.rs-5390395/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Revision requested\",\"date\":\"2024-11-14T10:02:57+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2024-11-07T19:36:42+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2024-11-04T22:13:11+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Journal of Nanoparticle Research\",\"date\":\"2024-11-04T19:09:53+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"journal-of-nanoparticle-research\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"nano\",\"sideBox\":\"Learn more about [Journal of Nanoparticle Research](http://link.springer.com/journal/11051)\",\"snPcode\":\"11051\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11051/3\",\"title\":\"Journal of Nanoparticle Research\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false}}],\"origin\":\"\",\"ownerIdentity\":\"419d07aa-746b-43ea-8a41-8facf6acd611\",\"owner\":[],\"postedDate\":\"November 18th, 2024\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2025-04-21T16:03:46+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-5390395\",\"link\":\"https://doi.org/10.1007/s11051-025-06305-2\",\"journal\":{\"identity\":\"journal-of-nanoparticle-research\",\"isVorOnly\":false,\"title\":\"Journal of Nanoparticle Research\"},\"publishedOn\":\"2025-04-14 15:57:37\",\"publishedOnDateReadable\":\"April 14th, 2025\"},\"versionCreatedAt\":\"2024-11-18 17:38:59\",\"video\":\"\",\"vorDoi\":\"10.1007/s11051-025-06305-2\",\"vorDoiUrl\":\"https://doi.org/10.1007/s11051-025-06305-2\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-5390395\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-5390395\",\"identity\":\"rs-5390395\",\"version\":[\"v1\"]},\"buildId\":\"qtupq5eGEP_6zYnWcrvyt\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}