France



&lt;i&gt; &lt;/i&gt;&lt;br/&gt;Magnetocuring of carbon and glass fibers was performed using Curie temperature tuned magnetic nanoparticles (CNP) embedded in adhesives, aka magnetoadhesive. Interestingly, these fibers were cured under alternating magnetic field (AMF) within a few minutes.&lt;i&gt; In-situ&lt;/i&gt; heating of the magnetoadhesive were controlled by CNP loading and AMF strength. The heating of the CNP switches off above its Curie temperature, which prevents overheating. For the first time, custom made AC-magnetorheometry was employed to understand the kinetics of curing of the magnetoadhesive under AMF. The storage modulus of the magnetocured adhesive exceeded 10 MPa at shear strain of &amp;lt; 10%.&lt;br/&gt;&lt;br/&gt;&lt;i&gt;Introduction:&lt;/i&gt;&lt;br/&gt;Magnetic field activated adhesive curing, aka magnetocuring have recently been reported[1]. Magnetocuring overcomes the limitations of available curing techniques e.g. photocuring[2], snap-curing[3], and electrocuring[4], etc, it allows the adhesive to be activated on-demand when an alternating magnetic field is applied. Carbon fiber is increasingly being used to make lighter and stronger parts in many industries including aviation, automobile, marine, sports, defence, IT, etc.[5] However, in most of the applications, these fibers need to bond with suitable thermosets/thermoplastics in order to achieve high stiffness, for which thermal curing is required. Magnetocuring of carbon and glass fibers can be applied in a range of commercial applications. The present work addresses the design and application of one-pot epoxy adhesives by the ‘modifier’ methodology for on-demand contactless curing under alternating magnetic field (AMF).&lt;br/&gt;&lt;br/&gt;&lt;i&gt;Material and Methods:&lt;/i&gt;&lt;br/&gt;Curie nanoparticles (CNP) were synthesized by the hydrothermal method and functionalized using oleic acid and epoxy [1]. Functionalized CNP were mixed into commercial 1C epoxy adhesive and cured under an alternating magnetic field (AMF, 400 kHz, 140 Oe). The kinetic parameters, real-time properties of the adhesive and composite were evaluated using a custom made AC magneto-rheometry setup.&lt;br/&gt;&lt;br/&gt;&lt;i&gt;Results and Conclusions:&lt;/i&gt;&lt;br/&gt;Magnetoadhesive applied carbon and glass fibers were passed through the magnetic field generated solenoid coil and cured within 5 min (Fig. 1A). This fast curing is important for &lt;i&gt;in-line &lt;/i&gt;manufacturing of fiber based components. The magnetoadhesive property under AMF and at room temperature were studied using AC-magnetorheometry. The gelation point of the magnetoadhesive with 30&lt;i&gt;wt.%&lt;/i&gt; CNP was achieved within 70 s of AMF exposure (Fig. 1B and 1C). On applying the magnetic field, a decrease in the loss modulus (G’) and increase in the storage modulus (G’’) was observed due to the initiation of crosslinking and composite hardening. The storage modulus of the magnetocured adhesive was observed to be &amp;gt;10 MPa at shear strain of &amp;lt; 10% (Fig. 1C). These results suggest that magnetocuring is an attractive technology for in the sports goods, automotive, aerospace and medical industries. It offers an energy efficient, remote, and wireless method of on-demand adhesion by exploiting self-regulating Curie nanoparticles (CNP). Real time magnetorheology measurements were used to determine the properties, fast gelation within 70 s was observed..&lt;br/&gt;&lt;br/&gt;&lt;i&gt;Acknowledgement:&lt;/i&gt;&lt;br/&gt;Authors acknowledge the financial support from the Agency for Science, Technology and Research (A*Star) for the grant IRG17283008 “Microprocessor- based methods of composite curing.

**References:**

[1] R. Chaudhary, V. Chaudhary, R.V. Ramanujan, T.W.J. Steele, Applied Materials Today 21, 100824 (2020).&lt;br/&gt;[2] S.C. Ligon-Auer, M. Schwentenwein, C. Gorsche, J. Stampfl, R. Liska, Polymer Chemistry 7, 257-286 (2016).&lt;br/&gt;[3] X.K. Hillewaere, R.F. Teixeira, L.T.T. Nguyen, J.A. Ramos, H. Rahier, F.E. Du Prez, Advanced Functional Materials 24, 5575-5583 (2014).&lt;br/&gt;[4] J. Ping, F. Gao, J.L. Chen, R.D. Webster, T.W. Steele, Nature communications 6, 1-9 (2015).&lt;br/&gt;[5] C. Soutis, Materials Science and Engineering: A 412, 171-176 (2005).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d53ed9987bc3b153986b15a11f93643b.jpg)
Fig.1 Magnetocuring and AC-magnetorheology of composites. (A) Magnetocuring of carbon and glass fibers for &lt;i&gt;in-line&lt;/i&gt;manufacturing, (B-C) Oscillation and amplitude sweep of 30&lt;i&gt;wt.% &lt;/i&gt;CNP within epoxy adhesive.



INTERMAG 2021

 Magnetocuring and Magnetorheology of Composites

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Magnetocuring of carbon and glass fibers was performed using Curie temperature tuned magnetic nanoparticles (CNP) embedded in adhesives, aka magnetoadhesive. Interestingly, these fibers were cured under alternating magnetic field (AMF) within a few minutes. In-situ heating of the magnetoadhesive were controlled by CNP loading and AMF strength. The heating of the CNP switches off above its Curie temperature, which prevents overheating. For the first time, custom made AC-magnetorheometry was employed to understand the kinetics of curing of the magnetoadhesive under AMF. The storage modulus of the magnetocured adhesive exceeded 10 MPa at shear strain of &lt; 10%. Introduction: Magnetic field activated adhesive curing, aka magnetocuring have recently been reported[1]. Magnetocuring overcomes the limitations of available curing techniques e.g. photocuring[2], snap-curing[3], and electrocuring[4], etc, it allows the adhesive to be activated on-demand when an alternating magnetic field is applied. Carbon fiber is increasingly being used to make lighter and stronger parts in many industries including aviation, automobile, marine, sports, defence, IT, etc.[5] However, in most of the applications, these fibers need to bond with suitable thermosets/thermoplastics in order to achieve high stiffness, for which thermal curing is required. Magnetocuring of carbon and glass fibers can be applied in a range of commercial applications. The present work addresses the design and application of one-pot epoxy adhesives by the ‘modifier’ methodology for on-demand contactless curing under alternating magnetic field (AMF). Material and Methods: Curie nanoparticles (CNP) were synthesized by the hydrothermal method and functionalized using oleic acid and epoxy [1]. Functionalized CNP were mixed into commercial 1C epoxy adhesive and cured under an alternating magnetic field (AMF, 400 kHz, 140 Oe). The kinetic parameters, real-time properties of the adhesive and composite were evaluated using a custom made AC magneto-rheometry setup. Results and Conclusions: Magnetoadhesive applied carbon and glass fibers were passed through the magnetic field generated solenoid coil and cured within 5 min (Fig. 1A). This fast curing is important for in-line manufacturing of fiber based components. The magnetoadhesive property under AMF and at room temperature were studied using AC-magnetorheometry. The gelation point of the magnetoadhesive with 30wt.% CNP was achieved within 70 s of AMF exposure (Fig. 1B and 1C). On applying the magnetic field, a decrease in the loss modulus (G’) and increase in the storage modulus (G’’) was observed due to the initiation of crosslinking and composite hardening. The storage modulus of the magnetocured adhesive was observed to be &gt;10 MPa at shear strain of &lt; 10% (Fig. 1C). These results suggest that magnetocuring is an attractive technology for in the sports goods, automotive, aerospace and medical industries. It offers an energy efficient, remote, and wireless method of on-demand adhesion by exploiting self-regulating Curie nanoparticles (CNP). Real time magnetorheology measurements were used to determine the properties, fast gelation within 70 s was observed.. Acknowledgement: Authors acknowledge the financial support from the Agency for Science, Technology and Research (A*Star) for the grant IRG17283008 “Microprocessor- based methods of composite curing.

**References:**

[1] R. Chaudhary, V. Chaudhary, R.V. Ramanujan, T.W.J. Steele, Applied Materials Today 21, 100824 (2020). [2] S.C. Ligon-Auer, M. Schwentenwein, C. Gorsche, J. Stampfl, R. Liska, Polymer Chemistry 7, 257-286 (2016). [3] X.K. Hillewaere, R.F. Teixeira, L.T.T. Nguyen, J.A. Ramos, H. Rahier, F.E. Du Prez, Advanced Functional Materials 24, 5575-5583 (2014). [4] J. Ping, F. Gao, J.L. Chen, R.D. Webster, T.W. Steele, Nature communications 6, 1-9 (2015). [5] C. Soutis, Materials Science and Engineering: A 412, 171-176 (2005).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d53ed9987bc3b153986b15a11f93643b.jpg)
Fig.1 Magnetocuring and AC-magnetorheology of composites. (A) Magnetocuring of carbon and glass fibers for in-linemanufacturing, (B-C) Oscillation and amplitude sweep of 30wt.% CNP within epoxy adhesive.

technical paper

Cobalt ferrite nanoparticles (NPs) are competitive candidates in nanomedicine and biomedical applications, especially in the fields of magnetic drug delivery, magnetic resonance imaging, and separation and detection of biomolecules [1,2]. The reason behind is a suitable combination of excellent chemical and magnetic characteristics, such as a high chemical stability, surface active sites, and ease of synthesis and functionalization, together with a high anisotropy constant, a high coercivity, and a moderate saturation magnetization. However, in order to control the functional response of cobalt ferrite NPs, one of the biggest challenges is to quantitatively disentangle the dependence of the composition, structure, or surface chemistry onto the overall magnetic response. In this study we unravel the key role played by the Co2+ cations on the destabilization of the collinear ferrimagnetism in cobalt ferrite NPs, by combining an advanced synthesis approach with a broad set of world-class complementary local probes. A set of samples of monodispersed, 8 nm cobalt ferrite NPs of identical stoichiometry but with a progressive inclusion of structural defects was prepared [3,4]. SQUID magnetometry results show a rapid degradation of the collinear ferrimagnetism as the structural disorder increases within the NPs, and even samples that are almost free from crystallographic defects exhibit relatively large values of the high-field susceptibility suggesting the occurrence of canting at least for some of the cations and sites [5]. As local characterization probes, synchrotron-based, element-, valence- and site- specific X-ray spectroscopy and magnetometry on ensembles of NPs was combined with high resolution transmission electron microscopy of selected, individual NP (Fig. 1) [5]. The analysis of element-specific X-Ray Magnetic Circular Dichroism (XMCD) spectra and hysteresis loops for all cationic sites reveals that the collinear alignment of the Co2+ cations in octahedral sites is significantly more affected by the structural disorder than in any other cation. This is because structural defects cause local distortions of the crystal field acting on the orbital component of the cations, yielding effective local anisotropy axes that cause a prevalent Co2+ spin canting through the spin–orbit coupling, owing to the relatively large value of the partially unquenched moment of these cations, as found by XMCD. As the number of structural defects increases, the rest of the cations are progressively dragged off the ferrimagnetic alignment, being the Fe3+ cations in tetrahedral sites the last ones to be affected by the disorder because the canting takes place first in octahedral sites thanks to their smaller number of next-nearest neighbors in the tetrahedral sublattice [5]. Our results demonstrate the key role of the Co2+ cations on the destabilization of the collinear ferrimagnetism in Co-ferrite NPs as their crystalline quality worsens and may help clarify the often conflicting, large variability of magnetic properties in the literature of Co-ferrite NPs with slightly different structural features. Our work may provide new avenues to interpret and control the functional response of Co-ferrite NPs, of relevance in the fields of rare-earth free permanent magnets, biological separation and detection, or nanomedicine. Acknowledgements The work was supported by Spanish MCIU and AEI (MAT2015-68772-P; PGC2018-097789-B-I00) and European Union FEDER funds. M.E.T. acknowledges Spanish MINECO for the Ph.D. contract BES-2016-077527. A.F.R. and C.M. acknowledge the financial support from the EU CALIPSO Transnational Access programme. Part of this work was performed at the Swiss Light Source, Paul Scherrer Institut, Switzerland. The measurements at FEI TITAN3 of the Laboratorio de Microscopias Avanzadas (LMA), Instituto de Nanociencia de Aragon (INA), Universidad de Zaragoza, are also gratefully acknowledged. S.R.V.A. thanks the Swiss National Science Foundation for financial support under project Nr. 169467.

**References:**

[1] S. Y. Srinivasan, K.M. Paknikar, D. Bodas, et al. Applications of Cobalt Ferrite Nanoparticles in Biomedical Nanotechnology. Nanomedicine. Future Medicine Ltd. May 2018, pp 1221–1238. https://doi.org/10.2217/nnm-2017-0379. [2] S. Amiri, H. Shokrollahi, The Role of Cobalt Ferrite Magnetic Nanoparticles in Medical Science. Materials Science and Engineering C. Elsevier January 2013, pp 1–8. https://doi.org/10.1016/j.msec.2012.09.003. [3] C. Moya, M. D. P.Morales, X. Batlle, A. Labarta, Phys. Chem. Chem. Phys. 17, 13143 (2015). [4] C. Moya, G. Salas, M. D. P. Morales, et al. J. Mater. Chem. C 3, 4522 (2015). [5] C. Moya, A. Fraile Rodríguez, M. Escoda-Torroella, et al., J. Phys Chem. C (2020) (in press). https://dx.doi.org/10.1021/acs.jpcc.0c06657.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/176a07ed0dc34fb44fc96344b80c0136.jpg)
Fig. 1. Monodisperse samples of 8 nm NPs with a tunable amount of structural defects prepared by thermal decomposition of Fe(III) and Co(II) acetylacetonates with a variable concentration of 1,2-hexadecanediol. HRTEM images and element-specific XMCD loops of the Co2+ cations corresponding to highly defective (a, c) and highly crystalline nanoparticles (b, d).

 Crucial Role of the Co Cations on the Destabilization of the Ferrimagnetic Alignment in Co-Ferrite Nanoparticles with Tunable Structural Defects

Iron oxide nanoparticles (NPs) have attracted a great attention for biomedical and environmental applications due to their good biocompatibility and magnetic performance. The control over the crystal structure and oxidation state are of paramount importance to optimize their properties [1, 2]. In this work we studied the effect of the amount of both 1,2-hexadecanediol and the solvent 1-octadecene on the thermal decomposition method with iron (III) acetylacetonate. On the one hand, a higher amount of one of the reagents gives rise to single-phase, single-crystal Fe3O4 NPs with diameters below 10 nm and narrow size distributions but with moderate reaction yields. On the other hand, low amounts of either of the two reagents result in large NPs containing both Fe3O4 and FeO phases but with high values of the reaction yield. Consequently, the samples exhibited two distinct magnetic behaviors depending on the amount of these two reagents. The hysteresis loops at room temperature for the small NPs showed the typical features of superparamagnetism: values of the saturation magnetization close to the bulk one for magnetite with no coercive field. On the contrary, larger NPs showed ferrimagnetic behavior with reduced values of the saturation magnetization, as well as shifted hysteresis loops at 5 K after field cooling the sample at 1 T. Zero-field cooling-field cooling (ZFC-FC) curves below 200 K for the small NPs exhibited a peak below room temperature corresponding to the blocking temperature, while those curves for the larger particles displayed two peaks at higher temperatures which can be associated with the Verwey and Neel transitions of magnetite and wüstite phases, respectively. This shows the biphasic nature of the large NPs. With this accurate monitoring of the reaction conditions we have added an extra level of optimization to the synthesis of these NPs. In particular, we have found that, for 1 mmol of iron (III) acetylacetonate, the minimum amounts of 1,2-hexadecanediol and 1-octadecene for the preparation of monophasic, single-crystale Fe3O4 NPs are 2.5 mmol and 5 mL, respectively. This allows us to tune the properties of each sample of iron oxide NPs to its specific application. [3] Acknowledgements The work was supported by Spanish MCIU and AEI (MAT2015-68772-P; PGC2018-097789-B-I00) and European Union FEDER funds. M.E-T. acknowledge Spanish MCIU for BES-2016-077527.

**References:**

[1] A. Fraile Rodríguez, C. Moya, M. Escoda-Torroella, A. Romero, A. Labarta and X. Batlle. J. Mater. Chem. C, 6, 4, 875–882 (2018). [2] C. Moya, M. P. Morales, X. Batlle and A. Labarta. Phys. Chem. Chem. Phys., 17, 19, 13143–13149 (2015). [3] M. Escoda-Torroella, C. Moya, A. Fraile Rodríguez, X. Batlle and A. Labarta. Langmuir (2020) doi.org/10.1021/acs.langmuir.0c02221

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/790431501f371d0ebef8ec3cb20fc3ab.jpg)
Colored HRTEM images of two samples synthetized with increasing amounts of 1,2-hexadecanediol and 1-octadecence and their respective magnetization curves, showing the correlation between low amount of both reagents and a defective crystal structure and a poorer magnetic behavior.

 Selective Control of Reagents as a Tuning Knob for Iron Oxide Nanoparticles with Controlled Morphology, Oxidation State and Magnetic Response

The heating ability of magnetic nanoparticles when subjected to alternating magnetic fields is a topic of interest for biomedical applications, as in the case of magnetic hyperthermia, and more recently in the area of induction heating in heterogeneous catalysis [1-2]. In particular, AC magnetometry stands out as a powerful technique to study the dynamic hysteresis loops of the nanoparticles in the desired medium and to quantify their heating efficiency, which is proportional to the area of the cycles. When properly calibrated, this device provides more accurate and reproducible measurements than the most widespread calorimetric method, giving also information about the magnetic properties of the system such as the coercive field, magnetization saturation and susceptibility. The study of the dynamic behaviour of systems of magnetic nanoparticles under radiofrequency fields is still being investigated both experimentally and theoretically [3-5], in particular the influence of nanoparticle dipolar interactions and chain formation, due to the huge increase in the heating efficiency reported in the literature. In this work, we perform an experimental systematic study of three samples of magnetite with sizes of 12 nm, 30 nm and 50 nm as a function of the applied field, the initial temperature of the sample and of the acquisition time. Time-dependent high-frequency hysteresis loop measurements are presented, showing that, in some cases, the hysteresis strongly depends on the acquisition time of the cycle, effect that can be associated to the chain formation. In the case of the 30 nm sample, there is a strong dependence of the hysteresis cycle shape with the acquisition time, increasing the area as well as the susceptibility as the acquisition time increases; whereas the 50 nm nanoparticles show always the same hysteresis cycles independently of the acquisition time (see Fig. 1). This effect is associated to the time required for the chain formation. Similar results have been already observed by Asensio et al., in iron carbide nanoparticles [1].

**References:**

[1] J.M. Asensio, et al., Nanoscale., Vol. 11(12), p.5402-5411 (2019) [2] B. Rivas-Murias, et al., Angewandte Chemie., Vol. 132(36), p.15667-15672 (2020) [3] I. Morales, et al., Nanomaterials., Vol. 8(12), p.970 (2018) [4] I. Rodrigo, I. Castellanos-Rubio, E. Garaio, et al., International Journal of Hyperthermia., Vol. 31(1), p.976-991 (2020) [5] D.P. Valdés, E. Lima Jr, R.D. Zysler, E. De Biasi, Physical Review Applied., Vol. 14, p.014-023 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2f6401c65514349ed6ceb4b1826c577f.jpg)
Fig. 1. Evolution of the cycles as a function of the acquisition time between 5 ms and 10 s, for an applied field of 27 mT and 50.3 kHz.

 Time-Dependent AC Magnetometry of Magnetite Nanoparticles in the Monodomain-Multidomain Limit

Over the past decade, magnetic field-induced self-assembly of magnetic inorganic nanoparticles has been studied extensively for particles having different sizes and compositions. However, relatively little attention has been devoted to how the surface chemistry of polymer nanoparticles affects their self-assembly properties. Self-assembly of nanoparticles becomes more important because novel collective and exceptional properties can be produced in the ordered array of nanoparticles [1-3]. More recently, methods using external fields such as magnetic fields have emerged as key methods to direct the assembly of inorganic nanoparticles effectively [4, 5]. In this work, we present the first direct observation of polymer nanoparticle chain formation in a magnetic field based on temperature induced surface properties of the PNIPAM layer. The colloidally stable PNIPAM coated Iron Oxide Nanoparticles were successfully synthesized by using 7-nm magnetic iron oxide nanoparticles embedded in a PNIPAM-g-PGMA shell. This temperature responsive polymer (PNIPAM-g-PGMA) was synthesized by a simple polymerization reaction at 80 oC involving the anchoring of poly(N-isopropylacrylamide) (PNIPAM) chains onto the surface of poly(glycidyl methacrylate) (PGMA). The PGMA was used because it has been explicitly shown to have the epoxide functional groups groups [6] located in the loops and tails of the core macromolecule. This work was concerned with the capability of thermoresponsive polymer nanoparticles forming chains in an external magnetic field at 25 oC and 45 oC. Chain length and width information was measured using SEM and TEM. The time-series experiment performed enabled the measurement of proton transverse relaxation rates with the magnitude of the fractional reduction in R2 being observed to decrease as the concentration of iron in polymer nanoparticles decreased for both temperatures. At 45 oC, we obtained more nanosized chain-like structures of PNIPAM-g-PGMA-NPs, which contain wider and longer chain-like substructures, owing to the hydrophobic properties of PNIPAM chain as shown in Fig. 1 (c). It is important to note that the magnetic properties of all the synthesized nanoparticles presented as superparamagnetic even after the surface was coated with PNIPAM- PGMA. The relevance of this work is that many applications of PNIPAM- PGMA coated magnetic nanoparticles are likely to involve the particles being exposed to strong magnetic fields. As such, a knowledge of the rates of chain formation and sizes of chains could be critical to predicting the behaviour of the flow of the particles in the blood stream, for example.

**References:**

[1] A.T. Ngo, M.P. Pileni, Nanoparticles of cobalt ferrite: Influence of the applied field on the organization of the nanocrystals on a substrate and on their magnetic properties, Advanced Materials, 12 (2000) 276-279. [2] S.H. Sun, C.B. Murray, Synthesis of monodisperse cobalt nanocrystals and their assembly into magnetic superlattices Journal of Applied Physics, 85 (1999) 4325-4330. [3] S. Wirth, S. von Molnar, M. Field, D.D. Awschalom, Magnetism of nanometer-scale iron particles arrays Journal of Applied Physics, 85 (1999) 5249-5254. [4] L.G. Paterno, E.H.C.P. Sinnecker, M.A.G. Soler, J.P. Sinnecker, M.A. Novak, P.C. Morais, Tuning of magnetic dipolar interactions of maghemite nanoparticles embedded in polyelectrolyte layer-by-layer films, Journal of Nanoscience and Nanotechnology, 12 (2012) 6672-6678. [5] C. Hoffmann, E. Mazari, S. Lallet, R.L. Borgne, V. Marchi, C. Gosse, Z. Gueroui, Spatiotemporal control of microtubule nucleation and assembly using magnetic nanoparticles, Nature Nanotechnology, 8 (2013) 199-205. [6] N.I. Taib, Vipul Agarwal, Nicole M. Smith, Robert C. Woodward, Timothy G. St Pierre, and K. Swaminathan Iyer. , Direct correlation of PNIPAM thermal transition and magnetic resonance relaxation of iron oxide nanoparticles., Materials Chemistry Frontiers 1(2017) 2335-2340.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eb66df8daf98544b300a29e7409203cd.jpg)
Fig. 1. TEM micrograph of the nanoparticles: (a) PNIPAM-PGMA-NPs and (d) PGMA-NPs in the absence of external magnetic field at 25 oC. Chain-like structures of PNIPAM-PGMA-NPs and PGMA-NPs at 25 oC (b and e) and 45 oC (c and f) in the presence of external magnetic field. Insets showing the details of the chain-like structures of nanoparticles. Scale bar: (a) 2 µm, (b) 5 µm, (c), (d), (e) and (f) 10 µm, (insets: (b), (e) and (f) 2 µm; (c) 5 µm).

 Chain Formation of PNIPAM coated Magnetic Nanoparticles in an External Magnetic Field and the Effect of Temperature

Bottom-up fabrication of magnetic nanostructures composed of particles with desired sizes and composition can result in significant magnetic properties desired for practical applications in high performing magnetics, spintronics, and magnetic sensors [1, 2]. Magnetic and magneto-transport properties are strongly size-dependent, and the ability to adjust nanoparticle size leads to a high control on nanostructures' behavior [3, 4]. Generation of nanoparticles by aerosol methods provides great control of particle formation, size and deposition [5, 6]. Here, we present a novel bottom-up approach for generating self-assembled magnetic nanostructures [7]. The method uses an aerosol technique based on spark ablation to produce nanoparticles (NPs) with tunable compositions guided onto any substrate of choice using combined electric and magnetic fields. Using external magnetic fields, magnetic NPs can be assembled one-by-one along any direction to form 1, 2, or 3-D structures, see Fig. 1. In these systems, both shape and magneto-crystalline contributions play a key role in the magnetic anisotropy resulting in enhanced magnetic properties such as higher coercivity [8]. The presented technique provides a new approach for self-assembling of 1, 2, and 3-D magnetic nanostructures with building blocks that can be tailored for a specific application. Fig. 1 (a-c) shows the magnetic-field-induced self-assembly of vertical and in-plane structures. The magnetic field used to control the self-assembly also aligns the easy axis of the NPs, resulting in a higher anisotropy compared to a chain with randomly oriented particles. Fig. 1 (d) shows the possibility of particle size modulation, which is similar to diameter modulation in magnetic nanowires [9]. As illustrated in Fig. 1 (e), these structures can be directly integrated on the suitable substrates for, e.g., transport measurements or practical applications, which suggests a great advantage over the common solution-based methods [10]. Furthermore, the particle generation technique can be used to generate a vast number of material systems that can be used as building blocks. We have produced nanochains (NCs) composed of Ni, Fe, Co [7, 11], and as shown in Fig. 1 (f, g), CoPd (alloy) and CoAu (segmented/1D granular) structures. By tuning the segmented structures or chemical composition of alloys, a variety of systems can be achieved with possible applications in magnetism and spintronics [5]. Fig. 2 shows the NCs transferred to a carbon-supported copper grid where they were imaged using SEM (a & d) and by Scanning Transmission X-ray Microscopy (STXM) using circular polarized X-rays. The measurements were performed at the PolLux beamline at the Swiss light source (SLS) [12]. X-ray magnetic circular dichroism (XMCD) provides magnetic contrast (b-c & e-f) with a resolution approaching that of a single particle when combined with SEM images from the same NC. Applying a strong ex-situ magnetic field produces a mostly homogeneous remanent magnetization along the NCs with only minor indications of domain formation. Applying an in-situ field of -140 mT resulted in that the XMCD contrast of several more regions along the NC turned bright. These results demonstrate that an ex-situ field can produce a strong remanent magnetization and that the weak in-situ fields can be used to switch the magnetization in some regions. It is argued that these observations are due to larger multi-domain particles that behave as nucleation centers to initiate domain formation. As shown in Fig. 2 (g), micromagnetic simulations on NCs show that the magnetization is energetically favorable along the long axis of the chains and in the same direction (single domain). However, when there is a particle with a diameter larger than the single domain size, the NC breaks up into two domains. Magneto-transport in these structures is of interest since the magnetized and demagnetized states of the chains can result in a magnetoresistance response, and also, the segmented chains composed of different materials (Such as Co/Au in Fig. 1) can act as 1-D magnetic multilayers. To investigate the magneto-transport in these systems, NCs are self-assembled directly onto the surface of a Si-chip insulated with SiO2 and pre-patterned with aligned markers. Contacts to the NCs are defined via electron beam lithography and thermal evaporation, and magneto-transport properties along with micromagnetic simulations will be discussed.

**References:**

[1] H. Wang, Y. Yu, Y. Sun, Nano, Vol. 6, p. 1-17 (2011) [2] D. Lisjak, A. J. P. i. M. S. Mertelj, Progress in Materials Science, Vol. 95, p. 286-328 (2018) [3] J. Mohapatra, M. Xing, J. Elkins, Journal of Physics D, Vol. 53, p. 504004 (2020) [4] Z. Xiang, Y Song, D Pan, Journal of Alloys and Compounds, Vol. 744, p. 432-437 (2018) [5] C. Preger, C. Bulbucan, B. O. Meuller, The Journal of Physical Chemistry C, Vol. 123, p. 16083-16090 (2019) [6] J. Fang, , L Schlag, SC Park, Advanced Materials, Vol. 28, p. 1770-1779 (2016) [7] C. Preger, M. Josefsson, R. Westerström, M. E. Messing, Nanotechnology (Submitted Article) (2021) [8] S. Singamaneni, V. N. Bliznyuk, C. Binek, Journal of Materials Chemistry, Vol. 21, p. 16819-16845 (2011) [9] L. A. Rodríguez, C. Bran, D Reyes," ACS nano, Vol. 10, p. 9669-9678 (2016) [10] X. Chen, Z. Zhou, H. E. Karahan, Small, Vol. 14, p. 1801929 (2018) [11] A. Schmidt-Ott, Spark Ablation: Building Blocks for Nanotechnology. CRC Press (2019) [12] J. Raabe, G Tzvetkov, U Flechsig, Review of scientific instruments, Vol. 79, p. 113704 (2008)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c295a21c34ef6fdff44b2922c6d85a95.jpg)
Fig. 1. SEM image of a single vertical nanochain (NC) (a), 2-D chains along the surface of the substrate (b), and 3-D self-assembly of Co nanoparticles (c). Nanochains with particle-size modulation (d), direct integration of NCs on a Chip (e). EDS (energy-dispersive X-ray spectroscopy) mapping of a CoPd alloy (f) and CoAu segmented (g) nanochain.

![](https://assets.underline.io/uploads/markdown_image/1/image/e10ee3f10149d6228d9b0e2b9546b632.jpg)
Fig. 2. SEM image of a nanochain (a) and corresponding XMCD contrast in a field of +140 mT (b) and -140 mT (c). SEM (d) and remanent XMCD contrast after magnetizing ex-situ in +1.5 T (e). XMCD contrast after applying an in-situ field of -140 mT (f). Micromagnetic simulation of a chain composed of magnetic single-domain particles and a chain including a particle larger than the single-domain size.

 Engineered Self-assembled Magnetic Nanochains INVITED

Cylindrical magnetic nanowires (NWs) are promising candidates for building blocks of 3D nanoarchitectures and 3D nanotechnologies [1,2]. They present great potential for 3D applications, offering responses to many external (electrical, magnetic, mechanical, thermal, etc.) stimuli [3]. The emerging interest toward cylindrical magnetic NWs is related to the fact that their geometry promotes topologically non-trivial 3D magnetic structures such as Bloch-point domain walls, complex configurations that connect vortex domains with opposite chirality, vortices or skyrmion tubes [4,5]. Here, we present a study on multisegmented NWs formed by ferromagnetic (FM) segments separated either by a different FM material or a non-magnetic (NM) one. On one hand we have alternating CoNi/Ni segments (Fig. 1 (a)), where the domain structure can be tailored by alternating magnetocrystalline anisotropy and the length of each segment. On other hand, FeCo ferromagnetic layers separated by thin Cu NM layers (Fig. 1 (c)). The multisegmented NWs were prepared by electroplating filling the pores of anodic aluminum oxide membranes. The HRTEM analysis confirms the multisegmented morphology with a uniform diameter, and periodic and sharp interfaces. Quantitative analysis reveals that the diameter of CoNi/Ni NWs is about 140 nm with lengths between 0.6 μm and 1.4 μm for CoNi and 1 μm for Ni segments while FeCo/Cu wires with 165 nm in diameter are formed by FeCo segments with 250 nm in length separated by 50 nm Cu layers. XMCD-PEEM imaging of multisegmented CoNi/Ni NWs reveals that the magnetic structure in Ni segment is in a dominantly axial magnetic state while in CoNi segments it depends on their length. In NWs with the shortest CoNi segments (0.6 μm), we observed single vortex domains, in longer segments of 1.2 μm we observed one to three vortex domain states (Fig. 1 (a)), while in the NWs with the longest CoNi segments either multi-vortex or multi-transverse domains were observed. The micromagnetic simulations show that the remanent magnetic structure of CoNi segments depends on the direction of the previously applied field. If the direction is perpendicular to both the NW and the magnetization easy axis, the vortex domains simply expand inside the segment following the structures formed at the interfaces and resulting in one vortex domain for short segments and two or more vortex structures for longer segments. In turn, when the field is applied perpendicular to the NW but along the magnetization easy axis, transverse domains are formed. They are separated by vortex domain structures with core at the surface pointing perpendicular to it. Furthermore, although Ni segments are in an almost single-domain state, they are not completely saturated, and present a small magnetization curling on the NW surface. Their chirality is formed prior to formation of magnetic structures in CoNi and imprints the chirality along the next CoNi segments (Fig. 1 (b)) [5]. The second investigated multisegmented system, FeCo/Cu (Fig. 1 (c-d)), presents a tilt at the interface between FM/NM layer. From the XMCD-PEEM images (Fig. 1 (c)) we determined that each FeCo segment presents a single vortex state which switches its magnetization under the influence of perpendicular magnetic fields. This switching is sequential and each segment has a slightly different switching field. The simulations (Fig. 1 (d)) unveil the main differences between magnetization states when the field is applied along different directions with respect to the NW axis. The tilt between adjacent segments breaks the rotational symmetry providing different magnetic potentials for vortices moving in a certain direction under the influence of applied magnetic field. The proper design of segments anisotropy and geometry (e.g., surface tilting) in cylindrical multisegmented nanowires opens multiple opportunities for advanced nanotechnologies in 3D magnetic nanostructures.

**References:**

[1] Fernández-Pacheco, A.; Streubel, R.; Fruchart, O.; Hertel, R.; Fischer, P.; Cowburn, R. P. , Nat. Commun. 2017, 8, 15756. [2] Hertel, R, Spin 2013, 03 (03), 1340009. [3] “Magnetic Nano- and Microwires: Design, Synthesis, Properties and Applications”, Elsevier 2020, edited by M.Vazquez. [3] Da Col, S.; Jamet, S.; Rougemaille, N.; Locatelli, A.; Mentes, T. O.; Burgos, B. S.; Afid, R.; Darques, M.; Cagnon, L.; Toussaint, J. C.; et al. , Phys. Rev. B 2014, 89 (18), 180405. [4] Fernandez-Roldan, J. A.; Perez del Real, R.; Bran, C.; Vazquez, M.; Chubykalo-Fesenko, O., Nanoscale 2018, 10 (13), 5923–5927. [5] Bran, C.; Fernandez-Roldan, J.A.; P Del Real, R.; Asenjo, A.; Chen, Y.-S.; Zhang, J.; Zhang, X.; Fraile Rodríguez, A.; Foerster, M.; Aballe, L.; et al. , ACS Nano 2020, 14, 12819.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9345e275af7517d8247f940544434392.jpg)
Figure 1. Schematic illustrations of multisegmented NWs (top panels) (a) Chemical contrast and XMCD-PEEM images of a CoNi (1.2 μm)/Ni(1 μm) multisegmented NWs (b) Modelled magnetization state of the CoNi/Ni NW presented in (a), (c) XMCD-PEEM images of FeCo/Cu NWs measured in remanence after perpendicular magnetic fields were applied, (d) Simulated magnetization configurations of FeCo/Cu NW before (upper panel) and after (bottom panel) magnetic fields were applied in y-direction. Scale bar 1μm.

 Controlled magnetization by magnetic fields in multisegmented cylindrical nanowires

Cylindrical magnetic nanostructures are attracting much interest in a wide range of applications (biomedical imaging, drug delivery, 3D memory storage devices, sensors, etc.). The ability to tune their magnetic properties by changing the geometry (disks, dots, wires, tubes), combined with low-cost and high-yield template fabrication methods, makes these nanostructures highly attractive for implementation in emerging technologies. However, most applications require a full understanding of the magnetization reversal mechanisms. Although it is a well-known topic, thoroughly studied for the past two decades, recent advances in characterization and micromagnetic simulation techniques renewed the attention of the scientific community towards the complete understanding of such magnetic 3D nano-elements [Bran2016, Fernández-Pacheco2017, Charilaou2018, Ruiz-Gómez2020]. In particular, Ni nanowires have been the most reported nanostructures fabricated in nanoporous alumina templates so far [Sousa2014, Proenca2012]. But, nanodisks and low-aspect ratio nanowires are still less explored, particularly regarding the full understanding of the magnetization reversal mechanisms. In this work, we have analyzed the magnetization response of cylindrical Ni nanostructures with 15 to 100 nm in diameter and 12 to 230 nm in length and compared our results with experimental data for periodic arrays. Our simulations show the presence of a critical diameter (d ≈ 30 nm) that determines the type of domain wall nucleated (transverse or vortex/skyrmion tube); and a critical length (L ≈ 100 nm) that limits the number of domain walls formed (one or two). By adjusting the diameter/length of the Ni nanocylinders, different magnetic remanent states and reversal mechanisms were observed (Figure 1). Moreover, vortex DWs were found to originate from 3D skyrmion tubes, which have been reported as one of the best configurations for magnetic storage devices. By increasing the diameter and aspect ratio (L/d) of nanowires with L &gt; 100 nm, three distinct reversal modes were observed: i) simultaneous propagation of two vortex DWs with opposite chirality; ii) propagation of only one vortex DW, or iii) spiral rotation of both DWs through the “corkscrew” mechanism (Figure 2). Only for very low aspect ratio structures (nanodisks), no skyrmion tubes were observed and reversal occurred by spiral rotation of one vortex DW. The broad range of dimensions studied in this work allowed the creation of the first complete magnetic phase diagram in cylindrical nanostructures [Proenca2021]. This universal phase diagram will be highly important for the future choice of nanoscaled dimensions in the development of novel nano-devices. This work has been supported by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 734801; by the Portuguese Fundação para a Ciência e Tecnologia (FCT) through the Investigador FCT program (Contract No. IF/01159/2015); by FCT and COMPETE 2020 (FEDER) under the projects POCI-01-0145-FEDER-028676, POCI-01-0145-FEDER-031302, POCI-01-0145-FEDER-032527, POCI-01-0145-FEDER-032257 and UIDB/04968/2020; and by the Spanish Ministerio de Ciencia e Innovación under the project MAT2017-87072-C4-3-P.

**References:**

C. Bran, E. Berganza, E. M. Palmero, et al., J. Mater. Chem. C, Vol. 4, p.978 (2016) A. Fernández-Pacheco, R. Streubel, O. Fruchart, et al., Nat. Commun., Vol. 8, p15756 (2017) M. Charilaou, H. B. Braun and J. F. Löffler, Phys. Rev. Lett., Vol. 121, p.97202 (2018) S. Ruiz-Gómez, C. Fernández-González, E. Martínez, et al., Nanoscale, Vol. 12, p.17880 (2020) C. T. Sousa, D. C. Leitao, M. P. Proenca, et al., Appl. Phys. Rev., Vol. 1, p.031102 (2014) M. P. Proenca, C. T. Sousa, J. Ventura, et al., Electrochim. Acta, Vol. 72, p.215 (2012) M. P. Proenca, J. Rial, J. P. Araujo and C. T. Sousa, Magnetic reversal modes in cylindrical nanostructures: from disks to wires, submitted (2021)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/224d41da086e562fd530d5cd1dca0bff.jpg)
Figure 1: Phase diagram of the magnetization reversal modes in individual Ni nanocylinders with different lengths and diameters, when applying the magnetic field along the nanocylinder’s length (parallel direction). Insets show selected cross-sectional representations of the magnetic configuration during reversal.

![](https://assets.underline.io/uploads/markdown_image/1/image/458fea4fee1b4edbee176c880e9b95e1.png)
Figure 2: 3D representation of the magnetic configuration during reversal of the simulated Ni nanowire with 100 nm in diameter and 130 nm in length illustrating the spiral rotation of two vortex domain walls (skyrmion tubes) through the “corkscrew” mechanism when applying the magnetic field along the z-direction (parallel to the nanowires’ long axis).

 Phase Diagram of Magnetization Reversal Modes in Cylindrical Ni Nanowires

Three-dimensional (3D) nanomagnets provide a great potential to be implemented in future spintronic devices for high-density magnetic memories, nano-sensing or logic. Among these appealing architectures, ferromagnetic nanotubes (NTs) are currently being investigated for their fast and low-power domain wall conduit properties [1]. The development of novel 3D nanostructures typically requires complex synthetic methods. Moving forward in this challenging task, Focused Electron Beam Induced Deposition (FEBID) has been explored for the growth of 3D ferromagnetic NTs. This unique one-step nanolithography technique, based on the decomposition of organometallic precursor gas molecules in the vicinity of a substrate [2,3], has demonstrated great versatility in terms of shape, composition and magnetic properties [4]. Following the strategy developed for the fabrication of core-shell nanowires [5], the growth of 3D Co NTs by FEBID has been performed for the first time [6]. The heterostructured design is composed by a vertical Pt-C nanowire (≤100 nm in diameter) acting as a core, and a Co coating forming the shell with a thickness down to ~11 nm. These are exotic magnetic nanostructures in which unconventional domain walls are formed, presenting high domain wall velocities without Walker breakdown phenomenon and where great stability during propagation has been predicted. Furthermore, Transmission Electron Microscopy (TEM) experiments reveal that these NTs present a nanocrystalline structure and a metallic content of ~70 at. %. In addition, a coercivity of ~16 mT has been obtained by Magneto-Optical Kerr Effect magnetometry, and magnetic characterization performed by Electron Holography evidences the ferromagnetic behaviour, estimating a remanent magnetic induction up to 1.3 T and detecting complex head-to-head magnetic domain walls. The application of magnetic fields inside the TEM has allowed the pinning and imaging of domain walls in these nanostructures. Finally, micromagnetic simulations have been performed for a deeper understanding of the magnetization dynamics [6].

**References:**

[1] R. Hertel, J. Phys.: Condens. Matter, 28, 483002 (2016). [2] J. Pablo-Navarro, S. Sangiao, C. Magén, et. al., Nanofabrication: Nanolithography techniques and their applications. Edited by J. M. De Teresa, IOP Publishing (2020). [3] A. Fernández-Pacheco, L. Skoric, J. M. De Teresa, et. al., Materials, 13, 3774 (2020). [4] J. Pablo-Navarro, D. Sanz-Hernández, C. Magén, et al., J. Phys. D. Appl. Phys., 50, 18LT01 (2017). [5] J. Pablo-Navarro, C. Magén and J. M. De Teresa, Nanotechnology, 27, 285302 (2016). [6] J. Pablo-Navarro, et al., manuscript in preparation.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fee42b13b0eb696628dd941a85be6a72.jpg)
Fig. 1. (a) HAADF-STEM image of a Co-FEBID NT cross-section. (b,c) Experimental and simulated magnetic phase shift around a domain wall obtained by Electron Holography and micromagnetic simulations, respectively. (d) Spin configuration obtained from micromagnetic simulations.

 Ferromagnetism of Single Vertical Cobalt Nanotubes Grown by Focused Electron Beam Induced Deposition

Bringing nanomagnetism into the third dimension is of growing interest due to many advantages that three-dimensional (3D) structures provide. The introduction of 3D geometrical effects such as curvature and chirality1, as well as the high density and enhanced device connectivity, lead to many opportunities for new physics and applications2,3. When we combine this promising field of 3D nanomagnetism with the well-established field of spintronics, a number of proposals ranging from the ultra-high-density 3D racetrack memory4 to 3D interconnected memristors for neuromorphic computing5 appear. However, before we can fully exploit the promise of 3D spintronics, significant advances in both the integration of 3D nanomagnets into 2D microelectronic circuits，and the understanding of the influence of a 3D geometry on the magnetotransport properties, are required. The implementation of 3D nanomagnetic circuits faces great challenges regarding the fabrication of a 3D nanostructure and its interconnectivity to the electronic components. Until recently, most magnetotransport experiments have concerned cylindrical nanowires, with complex micromanipulations needed to electrically contact them6. In this work, we employ 3D nano-printing capabilities provided by Focused Electron Beam Induced Deposition (FEBID)7, to directly fabricate a high-quality 3D Cobalt nanobridge with well-defined leads on pre-synthesized electrical contacts (Figure 1a). The SEM image shown in Figure 1b demonstrates the successful integration of this complex, high-aspect-ratio 3D nanostructure onto lithographically patterned electrodes. This printed 3D nanomagnetic circuit allows four-probe transport measurements with which we can probe the magnetotransport properties of the 3D nanostructure - and determine the influence of the three-dimensionality on these properties. To fully characterise the magnetotransport (MT) properties of the 3D magnetic nanobridge, we measured MT hysteresis loops for fields applied in different directions in three-dimensions (Figure 2a, b). These magnetotransport measurements, in combination with macrospin and finite element simulations, reveal that the three-dimensional structure of the nanobridge directly affects the magnetotransport in several ways. Firstly, the non-collinear current path in the 3D geometry results in a complex superposition of different MT effects, leading to an unusual angular dependence of well-known effects such as the Anomalous Hall effect. Secondly, we also identify a significant angular-dependence of the magnetoelectric signal due to the magnon magnetoresistance. This strong angular dependence occurs due to the strong influence of the demagnetising field within the non-collinear regions of the 3D geometry, highlighting the importance of magnetostatics in 3D nanostructures8. These new insights into the influence of a 3D geometry on the magnetotransport effects reported in this work provide the basis for the future study of new spintronic effects in 3D magnetic nanostructures, as well as the realization of 3D spintronic technologies. This methodology shown here combining FEBID 3D printing and standard planar lithography can be extended to more complicated geometries and other materials, opening the door to the fundamental study of new phenomena that exploit the interplay between 3D geometry and magnetotransport and may find applications in the future of areas such as magnonics, frustrated magnetic systems, and magnetic neural networks.

**References:**

 (1) R. Streubel, P. Fischer and F. Kronast, J Phys D Appl Phys., Vol. 49, p.363001(2016) (2) A. Fernández-Pacheco, R. Streubel and O. Fruchart, Nat Commun., Vol. 8, p.15756 (2017) (3) P. Fischer, D. Sanz-Hernández and R. Streubel, Apl Mater., Vol. 8, p.15756 (2017) (4) S. Parkin, M. Hayashi and L. Thomas, Science., Vol. 320, p.190-194 (2008) (5) A. May, M. Hunt and A. Berg, Commun Phys., Vol. 2, p.13 (2019) (6) M. Schöbitz, A. Riz and S. Martin, Phys Rev Lett ., Vol. 123, p.217201 (2019) (7) L. Skoric, D. Sanz-Hernández and F. Meng, Nano Lett ., Vol. 20, p.184-191 (2019) (8) F. Meng, C. Donnelly and C. Abert, Arxiv., arXiv:2011.09199 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f82793d4777c5e628b8b37e46d66e2d7.jpg)
Fig.1 (a) 3D nano-printing of the bridge via Focused Electron Beam Induced Deposition (FEBID) on pre-patterned electrical contacts. (b) The SEM image of the as-fabricated nanomagnetic circuit. (c) Four-probe magnetotransport measurement configuration. (d) The SEM image of the top view of the nanobridge.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba14c1bac15d9b830f10e775d14b93fe.jpg)
Fig.2 (a) The schematic shows how the field was applied relative to the 3D nanobridge, θ is the angle between the applied field and the substrate (b) Magnetotransport hysteresis loop obtained from -4 T to 4 T and 4 T to -4 T for each field angle θ, from θ = 0° to θ = 90° (from violet to red).

 Non-planar geometrical effects on the magnetoelectrical signal in a 3D nanomagnetic circuit

Investigation of magnetic properties of nanostructured ferromagnets, such as oriented arrays of carbon nanotubes (CNTs) containing ferromagnetic nanoparticles (FNPs), is still relevant. In addition to attractive applications in magnetoelectronics, CNTs with embedded FNPs are also a very useful model object for studying magnetic interaction of the latter through a conducting medium. For this, it is important to establish a relation between macroscopic and microscopic parameters of the system. In nanostructured ferromagnets, this dependence is described within the random magnetic anisotropy model (RAM), in which the spin system and, consequently, the main macroscopic characteristics (coercivity, susceptibility, saturation magnetization) are determined by such microscopic parameters as the exchange interaction constant, FNP magnetization, local magnetic anisotropy constant and grain size 2Rc [1]. Recently, magnetic parameters like the exchange and anisotropy fields, effective magnetic anisotropy constant, Bloch and exchange constants in aligned CNT arrays containing FNPs were determined within the RAM by analyzing law of the approach to saturation magnetization and corresponding modeling of the correlation functions of the magnetic anisotropy axes of the FNPs [2,3]. Presence of the interplay between the exchange interaction and magnetic anisotropy, as well as the contribution of not only random, but also coherent anisotropy, was established [3]. In addition, the important role of magnetoelastic anisotropy in the case when a single FNP is localized inside a CNT has been revealed. [4]. It was shown also that aligned CNT arrays with a low concentration of FNPs embedded only inside CNT have relatively high values of exchange fields, random and coherent anisotropy. They are manifested in CNT arrays, in which the average distance between the FNPs significantly exceeds the size of the latter, reaching hundreds of nanometers. These effects, which do not currently have a convincing explanation, are mainly associated with the presence of the exchange interaction between FNPs through the CNT matrix. However, there is still no reasonable mechanism of the long-range exchange interaction in CNT arrays. In our work [5], it was assumed that these effects are related to the indirect exchange coupling of the RKKY type via the conducting electrons of CNTs. The obtained preliminary estimations have shown that the RKKY exchange interaction is enhanced by the presence of spin-orbit coupling (SOC) and could propagate up to a micrometer scale [5]. In this contribution a multiwall CNT (MWCNT) with embedded FNPs is considered. We present the results of modeling of the RKKY interaction in MWCNT depending on its diameter, chirality, chemical potential and SOC constant within the Klinovaya-Loss model [6]. The influence of the external longitudinal magnetic field is also studied. It is assumed that the main contribution to the RKKY interaction is caused by the conduction electrons of the inner wall of CNTs which is in contact with the FNP. In addition, spin-orbit interaction (SOI) in CNT is also considered. The SOI in a nanotube can occur due to the curvature effect, which significantly increases its contribution in comparison with a flat graphene. It can also be enhanced by FNP, CNT defects or impurity states. The spin susceptibility of CNT conduction electrons χ/χ0 is evaluated (χ0=a2kG/hυF, where υF is the Fermi velocity, kG is the circumferential direction, a is the lattice constant). Fast oscillations are excluded and only slowly changing envelopes of spin susceptibility are considered. The chemical potential is tuned inside the gap opened by SOI. It is shown that the decay of the amplitude of the χ/χ0 oscillations depends strongly on the chemical potential: the higher the Fermi energy of the CNT (εF), the more significant is the decay. The frequency of spin susceptibility oscillations increases with the increase of the εF (Fig. 1). This is due to the fact that with the increase of the Fermi energy of CNTs, the discrepancy between the gap opened by SOI and the value of chemical potential increases. Finally, the proposed approach allows evaluating the energy of the exchange interaction between FNPs belonging to the same CNT. The work is supported by the COST Action CA19118.

**References:**

[1] E.M. Chudnovsky, J. Appl. Phys., Vol. 64, p. 5770 (1988). [2] A.L. Danilyuk, A.L. Prudnikava, I.V. Komissarov, et al. Carbon, Vol. 68, p. 337 (2014). [3] A.L. Danilyuk, I.V. Komissarov, V.A. Labunov, et al. New J. Phys. Vol. 17, p. 023073 (2015). [4] S.L. Prischepa, A.L. Danilyuk, A.V. Kukharev, et al. IEEE Trans. Magn. Vol. 55, p. 2300304 (2019). [5] A.L. Danilyuk, I.V. Komissarov, A.V. Kukharev, et al. Europhys. Lett. Vol. 117, p. 27007 (2017). [6] J. Klinovaja and D. Loss D, Phys. Rev. B, Vol. 87, p. 045422 (2013).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/29f3738a3c00cb89dafac5b18dcdb897.jpg)
Fig. 1. Decay of the oscillation amplitude of the spin susceptibility χ/χ0 along the axis of the semiconductor CNT of diameter of 25 nm with chiral indices (235,129) and εF=18 (blue) and 30 (red) meV. The chirality angle is 39.54° and kG =0.053 nm-1.

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