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The magnetic anisotropy and the coercive field (H&lt;sub&gt;C&lt;/sub&gt;) are key properties of the magnetic nanoparticles (NPs) considering their applications in biomedicine, for drug delivery and magnetic hyperthermia, and for the development of free-rare-earth magnets. Cobalt ferrite (Co&lt;sub&gt;x&lt;/sub&gt;Fe&lt;sub&gt;3-x&lt;/sub&gt;O&lt;sub&gt;4&lt;/sub&gt;) nanoparticles exhibit the largest coercive field between all the Fe oxides nanoparticles with spinel structure. The large coercive property is correlated to the Co&lt;sup&gt;2+&lt;/sup&gt; contain, that gives rise to the single ion- anisotropy, but the role of other parameters like: cationic occupancy, structural quality, magnetic order, structure, particle size and morphology and surface properties, have been considered very important [1-4]. In general, to optimize and tailoring the magnetic properties of NPs annealing treatments are employed fruiting the thermal induced structural magnetic properties of Cobalt ferrite nanoparticles that is induced by an alternative solvent mediated annealing process in mild temperatures.&lt;br/&gt;Co&lt;sub&gt;0.4&lt;/sub&gt;Fe&lt;sub&gt;2.6&lt;/sub&gt;O&lt;sub&gt;4&lt;/sub&gt; nanoparticles of average size of 32 (8) nm were synthesized by thermal decomposition technique and further solvent mediated annealing at temperatures between 150-320° C. We obtain an important change of the coercive field but not of the remanence ratio neither the specific magnetization as function of the treatment temperature. The NPs annealed at 210 °C exhibit maximum H&lt;sub&gt;C&lt;/sub&gt; of 0.19 T with high specific magnetization (79 Am&lt;sup&gt;2&lt;/sup&gt;/kg) being the H&lt;sub&gt;C&lt;/sub&gt; almost 50% larger than the value of the as-prepared NPs (H&lt;sub&gt;C&lt;/sub&gt;=0.12T). A wide structural (XRD), morphological (HRTEM), chemical (Mossbauer) and magnetic characterization was performed to determine the main mechanism that gives rise to the coercive improvement. These characterizations exclude the role of the particle size, the particle morphology or the inversion degree in the magnetic changes. The analysis of the temperature dependence of the hysteresis and the remanence measurements do not evidence changes in the reversal process. Herein we demonstrate that a solvent mediated annealing treatment in mild conditions permits the reduction of the concomitant internal stresses generated during the nanocrystal growth.&lt;br/&gt;Therefore, the increase in the coercive field observed in the post treatment process in a solvent media increase substantially the performances of this type of material for the development of novel rare-earth free permanent magnets.&lt;br/&gt;This research was supported by EU- H2020 AMPHIBIAN Project (H2020-NMBP-2016-720853).

**References:**

[1] C. Moya et al. J. Mater. Chem. C 3, 4522 (2015)&lt;br/&gt;[2] A. López-Ortega et al., Chem. Mater. 27, 4048 (2016).&lt;br/&gt;[3] E. Lottini et al., Chem. Mater. 28, 4214 (2016).&lt;br/&gt;[4] A. López-Ortega, E. Lottini, G. Bertoni, C. de Julián Fernández, C. Sangregorio, Chem. Mater. 29, 1279 (2017).

**Images:**





INTERMAG 2021

 Magnetic Hardening of Cobalt Ferrite Nanoparticles by a controlled solvent-mediated annealing

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The magnetic anisotropy and the coercive field (HC) are key properties of the magnetic nanoparticles (NPs) considering their applications in biomedicine, for drug delivery and magnetic hyperthermia, and for the development of free-rare-earth magnets. Cobalt ferrite (CoxFe3-xO4) nanoparticles exhibit the largest coercive field between all the Fe oxides nanoparticles with spinel structure. The large coercive property is correlated to the Co2+ contain, that gives rise to the single ion- anisotropy, but the role of other parameters like: cationic occupancy, structural quality, magnetic order, structure, particle size and morphology and surface properties, have been considered very important [1-4]. In general, to optimize and tailoring the magnetic properties of NPs annealing treatments are employed fruiting the thermal induced structural magnetic properties of Cobalt ferrite nanoparticles that is induced by an alternative solvent mediated annealing process in mild temperatures. Co0.4Fe2.6O4 nanoparticles of average size of 32 (8) nm were synthesized by thermal decomposition technique and further solvent mediated annealing at temperatures between 150-320° C. We obtain an important change of the coercive field but not of the remanence ratio neither the specific magnetization as function of the treatment temperature. The NPs annealed at 210 °C exhibit maximum HC of 0.19 T with high specific magnetization (79 Am2/kg) being the HC almost 50% larger than the value of the as-prepared NPs (HC=0.12T). A wide structural (XRD), morphological (HRTEM), chemical (Mossbauer) and magnetic characterization was performed to determine the main mechanism that gives rise to the coercive improvement. These characterizations exclude the role of the particle size, the particle morphology or the inversion degree in the magnetic changes. The analysis of the temperature dependence of the hysteresis and the remanence measurements do not evidence changes in the reversal process. Herein we demonstrate that a solvent mediated annealing treatment in mild conditions permits the reduction of the concomitant internal stresses generated during the nanocrystal growth. Therefore, the increase in the coercive field observed in the post treatment process in a solvent media increase substantially the performances of this type of material for the development of novel rare-earth free permanent magnets. This research was supported by EU- H2020 AMPHIBIAN Project (H2020-NMBP-2016-720853).

**References:**

[1] C. Moya et al. J. Mater. Chem. C 3, 4522 (2015) [2] A. López-Ortega et al., Chem. Mater. 27, 4048 (2016). [3] E. Lottini et al., Chem. Mater. 28, 4214 (2016). [4] A. López-Ortega, E. Lottini, G. Bertoni, C. de Julián Fernández, C. Sangregorio, Chem. Mater. 29, 1279 (2017).

**Images:**

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In recent years, magnetic nanoparticles based on iron oxides have found increasing interest in practical applications in the field of biotechnology and biomedicine. Surface modified magnetic nanoparticles can be used for selective isolation of certain biomolecules, such as nucleic acids and proteins. The method, commonly known as "magnetic separation", has gained popularity in performing tests for diagnostic purposes. The aim of this work was to develop a nanomagnetic construction based on iron oxide nanoparticles for efficient separation of DNA molecules and subsequent investigation by polymerase chain reaction. The magnetic particles were prepared by coprecipitation from a solution of FeCl3 and FeCl2 salts in a molar ratio of 2:1 at room temperature. With constant stirring, an NH4OH solution (25%) was injected into the solution of iron salts until pH = 10 was reached. At the end of the reaction, the magnetic nanoparticles were collected using a magnet and washed several times in distilled water until pH = 7.0. To use nanoparticles in magnetic separation of DNA, we treated them with a solution containing 1.25 M sodium chloride and 10% PEG 6000 to inhibit free radical oxidation. For biomedical applications of magnetic nanoparticles, an important role is played by the blocking temperature - the temperature separating the hysteresis and hysteresis-free responses of an ensemble of particles. For applications such as bio-separation, blocking temperatures close to ambient (body temperature) are considered optimal. This choice is due to a compromise between the better colloidal stability of an ensemble of superparamagnetic particles (hysteresis-free behavior) and the high magnetic susceptibility of blocked nanoparticles (response with hysteresis). For magnetic characterization of our particles, we performed measurements of magnetization curves at various temperatures (Fig. 1). According to Fig. 1, the magnetic hysteresis disappears at temperatures above 100 K. The distribution of particles by size and by the magnitude of magnetic anisotropy can lead to inhomogeneity of the blocking temperature in the ensemble of particles. To quantify this inhomogeneity (blocking temperature distribution), we calculated the data in Fig. 1 by different methods. The temperature behavior of the coercive force in Fig. 2 does not follow the power-law dependence Hc(T)=Hc(0)*(1-(T/TB)α), (1) usually discussed for single-domain non-interacting nanoparticles at temperatures below the blocking temperature (TB) [1,2]. The power exponent α, in this case, is in the range from 0.67 to 1.00 [3,4]. This deviation may be due to the inhomogeneity of the blocking temperature in the system of the studied nanoparticles. Therefore, to describe the coercive force, we used averaging [5]: Hc(T)=Hc(0)*(∫Hc(T)*f(TB)dTB)/(∫(TB)*dTB) (2) where the parameter Hc(0) is the average coercive force at T = 0 K. Describing the experimental behavior of the coercive force by expression (2), we can determine the parameters of the distribution function f (TB) corresponding to the best description of the experiment. The best agreement is achieved using the lognormal distribution function: f(TB)=1/(TBσ√2π)*exp(-ln2(TB/TB0)/2σ2) with the parameters TB0 = 80 K, σ = 0.77. The study of the nanoparticles ability to isolate nucleic acids was carried out as follows. Leukocyte lysate from a blood sample obtained from a patient with chronic myeloproliferative disease was added to the nanoparticle suspension. Then, the nanoparticles bound to DNA molecules were separated using a magnet. Subsequent washing of DNA from nanoparticles was carried out with 70% ethanol at room temperature, then elution was carried out in 50 μl of TE buffer for 5 minutes at 65 °C. Real-time PCR reaction was performed using the resulting eluate to detect the JAK2 gene. As a comparison, a parallel reaction was carried out with DNA samples isolated by the sorption method using a commercial kit "DNA-Sorb-B" (Amplisens, Russia). The comparative concentration of the isolated DNA was 3.9 ng/μl with standard isolation and 2.4 ng/μl with isolation using magnetic nanoparticles. It follows from the PCR results that the proposed method for isolating DNA from human blood samples is not inferior in efficiency to the standard isolation method and does not affect the efficiency of PCR amplification. This work was supported by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund to the research projects No. 20-42-242902 and by the Council of the President of the Russian Federation for State Support of Young Scientists and Leading Scientific Schools (project no. MK-1263.2020.3). We are grateful to the Center of collective use of FRC KSC SB RAS for the provided equipment.

**References:**

[1] R.S. Iskhakov, S.V. Komogortsev, S.V. Stolyar et al. Met. Metallogr., 88, 261–269 (1999) [2] S. V. Komogortsev, R.S. Iskhakov, A.D. Balaev et al. Phys. Solid State. 49, 734–738 (2007) [3] H. Pfeiffer, Phys. Status Solidi. 118, 295–306 (1990) [4] I.S. Poperechny, Y.L. Raikher, V.I. Stepanov, Phys. B Condens. Matter., 435, 58–61 (2014) [5] S. V. Komogortsev, R.S. Iskhakov, A.D. Balaev et al., Phys. Solid State. 51, 2286–2291 (2009)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a142de32b117ade09ea1fdcd4dd6355f.jpg)
Fig. 1 Magnetization curves

![](https://assets.underline.io/uploads/markdown_image/1/image/a2a097a3f7750bc29552695db104a0b8.jpg)
Fig. 2. The temperature behavior of the coercive force (red symbols) is not described by equation (1) - dashed lines, but is described by equation (2) - solid line.

 Structure and Magnetic Properties of Maghemite Nanoparticles for DNA Extraction

To separate magnetically coupled particles on lab-on-a-chip devices, microfluidic magnetophoresis plays a pivotal role [1]. It can be useful for biomedical applications like cancer detection, drug delivery, screening, clinical diagnostics [2, 3]. When subjected to a non-uniform magnetic field, small-sized (μm-nm) particles suspended in a fluidic medium will translate toward either the maxima or minima of the gradient of the magnetic field. However, it is very difficult to produce high-gradient magnetic field at micro-scale due to several issues such as non-availability of integratable, high energy product permanent magnets and the detrimental effect of strong demagnetization field of the thin film magnets. Therefore, patterning the magnetic surface is required to produce high flux density with micro-scale resolution over large areas. The efficient design and optimization of such micro-magnetic structures along with their magnetic interaction play an important role in the development of the devices for microfluidic magnetophoresis applications. In our work, comparative FEM analysis is performed to show the advantages of using micro-patterned magnets over bulk rectangular magnet for microfluidic magnetophoresis applications, which is also validated using an analytical framework. The width (x-axis) and height (y-axis) of microfluidic channel were considered 1200 µm and 100 µm respectively with varying gap distance from the permanent magnetic structures (Fig. 1(a)). We have considered bulk rectangular magnetic structure of 1000 µm width and a variation in the height from 100 to 500 µm. Micro patterned rectangular magnets, with 50 µm fixed gap distance between succesive patterns, across the width of microfluidic channel are also analyzed to study the advantage of micro-patterned magnets over bulk rectangular magnet as shown comparatively in Fig. 1(b) and (c). All proposed magnetic structures were concocted using a nano-composite of NdFeB magnetic powder embedded in Polydimethylsiloxane (PDMS) matrix. Geometric optimization of the entire structure including the separation size, height, and width of the separate features are explored using FEM and analytical models to efficiently control the particle trajectories within the microfluidic channel. Effect of different geometries (rectangle, square, triangular etc.) of the micro-patterned magnets are also determined by a factor (H●▽) H, which is proportional to the magnetic force and describe the range of impact of magnets [4]. At the various height (wg=50μm, 80μm, 110μm) from the micro-magnet structure, the magnetic flux densities Hx and Hy were extracted and subsequently used in an customized MATLAB code to determine the force Fx and Fy for describing the motional behavior of magnetic particles in the channel with the help of Newton’s second law. A wide magnet comparable to the microfluidic channel can yield a pseudo magnetic field which can magnetize the micro/nano particles in the channel but does not cause cumulative forces, being exerted on them which can be greatly enhanced by using optimized micro-patterns as shown in Fig. 2. Proof-of-concept prototype of the proposed device is being fabricated using standard micro-fabrication processes. Overall, an effective design methodology for developing highly efficient micro-magnetic flux sources is described which can be useful in many micro-scale applications including biological particle separation and mixing.

**References:**

1. R. Zhou, Q. Yang, F. Bai, J. A. Werner, H. Shi, Y. Ma, C. Wang, Microfluid. Nanofluid., 20, 110 (2016). 2. R. Zhou, A. N. Surendran, M. Mejulu, Y. Lin, Micromachines, 11,129. 25 (2019). 3. F. Alnaimat, S. Karam, B. Mathew, B. Mathew, IEEE Nanotech. Mag., 14(3), 24-41 (2020). 3. E. P. Furlani, J. Appl. Phys., 99, 024912 (2006).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c7e9be793ad6286fdc706ad5898f152d.jpg)
Fig. 1: (a) Proposed device architecture. FEM simulation results of the y component of magnetic flux density in the microfluidic channel due to rectangular magnet of size (b) 1000×100 µm2 (bulk magnet) and (c) 100×100 µm2 (micro-patterned magnets) with 50 µm pattern gap. A thin film (b) produces magnetic field only at the edges whereas the magnetic flux density vis-à-vis the magnetic flux gradient can be significantly improved through micro-patterning (c) of the magnetic surface.

![](https://assets.underline.io/uploads/markdown_image/1/image/32ee19bb927965e9321dee559a17f72e.jpg)
Fig. 2: The Y component of (a) magnetic field intensity (Hy) and (b) Force (Fy) exerted on the particles inside the microfluidic channel at different height (ht.) due to single bulk and patterned micro-magnets.

 Design and Analysis of High-gradient Magnetic Field Source at Micro-scale for Microfluidic Magnetophoresis Applications

Magnetic nanostructures attract considerable scientific and technological efforts in diverse applications, such as magnetic recording, magnetic sensors, biomedicine, etc.[1,2] Whereas patterned nanomagnets are mostly 2D planar structures, recently research has been expanded into 3D aspect. In 3D nanomagnets, more delicate and complicated magnetic configurations, with novel properties, become possible. [3,4] Imaging and understanding the magnetic configurations in 3D nanomagnets is an increasingly important issue for a wide range of modern applications. Here, aligned, isolated iron nanocuboids [Fig. 1 (a)] have been fabricated by taking advantage of epitaxial, three-dimensional-island growth on GaAs(001) during electrodeposition at low deposition rates.[5] The nanoparticles exhibit lateral size between 10 and 250 nm and heights below 80 nm. Surface {100} facets predominate with a thin crystalline oxide shell that protects the nanoparticles during prolonged storage in air [Fig. 1 (b)]. The magnetic configurations inside the cuboids are systematically investigated by combining quantitative magnetic force microscopy (qMFM) with micromagnetic simulations [Fig. 1 (c, d)]. Experimental results and micromagnetic simulations give evidence for a transition from single-domain state to vortex state, and even to Landau pattern with increasing the size of the cuboids, demonstrating the key importance of nanometric size control of magnetic nanoparticles. The simulated and experimental magnetic charge profiles are compared and show good agreement [Fig. 1 (e-h)]. Such measurements open the door to fine tuning the magnetic configuration of nano-objects that will find applications in fields of sensor, magnetic recording, and biomedicine.

**References:**

1. C. Gatel, F. J. Bonilla, A. Meffre, et al. Nano Lett. 2015, 15, 6952−6957. 2. M. Bode, A. Wachowiak, J. Wiebe, et al. Appl. Phys. Lett. 2004, 84, 948−950. 3. L. A. Fomin, I. V. Malikov, S. V. Pyatkin, et al. J. Magn. Magn. Mater. 2010, 322, 851−857. 4. F. J. Bonilla, L.-M. Lacroix, T. Blon, J. Magn. Magn. Mater. 2017, 428, 394−400. 5. K. Leistner, M. Yang, C. Damm, et al. Nanoscale, 2017, 9, 5315–5322.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5a71d36f584e8493e8281fc8b8ff7eca.jpg)
Fig.1 (a) SEM image showing isolated iron cuboids with different size distribution. (b) EELS mapping of Ga, Fe and O elements in iron cuboid. (c) qMFM scan of one cuboid with a lateral size of 54 nm, and the related micromagnetic simulation showing vortex state (d). Experimental MFM phase of one cuboid with a lateral size of 170 nm (e) and the calculated MFM phase (f). (g) Extracted profiles from (e) and (f), (h) Simulation of (e) showing Landau pattern.

 Size-specific magnetic configurations in epitaxial iron nano-cuboids

We aim to prepare a multifunctional application-ready material, which could be used as a sensing and simultaneous actuating device driven by shape memory processes. One of the most promising ways to expand the application possibilities of a well-known material is the down-sizing. Therefore, we have prepared Ni2FeGa Heusler-based nanowires and studied their magnetic properties. The Ni2FeGa Heusler alloy has a L21 structure and undergoes a martensitic transformation [1]. The martensitic transformation temperature of the Ni2FeGa Heusler alloy can be tuned by changing its chemical composition [2]. It also shows a shape memory and a multi-caloric behaviour. The nanowires that we have studied were prepared by a galvanostatic electrochemical deposition, using the anodized aluminium oxide (AAO) membrane with the nanopores diameter of 60 nm. The deposition time was adjusted to obtain nanowires of an appropriate length, which was 7.5 μm. The chemical composition of the prepared nanowires is Ni55Fe43Ga2. The deviation from the X2YZ Heusler chemical composition is probably due to the difficult determination of the effective deposition area of the AAO membrane. During the isothermal magnetization measurement (Fig. 1), a magnetic shape memory temperature region was defined. Between the temperatures of 290 and 360 K, an unusual magnetization increase was observed within each magnetization isotherm. The magnetization increase within the isothermal measurement or within the measurement of the hysteresis loops was ascribed to the magnetic shape memory behaviour within previous research of shape memory materials, such as the Ni2MnGa or Ni2MnSn [3, 4]. The observed magnetization increase occurs at different values of the applied transformation magnetic field. A deeper analysis shows that the transformation fields are temperature dependent. The temperature dependence of the transformation magnetic field can be described according to the Clausius-Clapeyron equation and a fitting model of the experimental data shows that the transformation temperature is ≈285 K and is also dependent on the system pressure. The shape memory behaviour of the prepared nanowires made them interesting for further analysis. Therefore, we have performed the First-Order Reversal Curve (FORC) analysis of the magnetic shape memory nanowires. The measurements of the individual FORCs were performed at four different temperatures, following the cooling behaviour of the isothermal magnetization measurement. The FORC measurements were performed at 395, 300, 200 and 100 K (Fig. 2). Each measurement shows a diverging FORC distribution, which was defined by Pike, et al. [5]. The contours within such diagram diverge from the Hu axis and intersect the Hc = 0 axis. The FORC distribution with the diverging shape shows that the nanowires array is a multi-domain and highly interacting system, as stated by Muxworthy, et al. [6]. In the hysteresis loops measurements, we show that the main contribution to the nanowires array magnetization process consists of the magnetostatic interactions of the neighbouring nanowires. The vertical spread of the FORC distribution is a function of the internal demagnetization field (magnetostatic interactions within the neighbouring nanowires), but it depends on several domain properties (domain cancelation, domain shape and domain wall interactions) [7]. However, the vertical spread of the diverging FORC distribution should increase with the system volume, which points to the shape changes that occur within the Ni55Fe43Ga2 nanowires. This was shown in the case of multi-domain magnetic nanoparticles with a strong domain wall pinning. During the investigation of a structure transformation of CoNi alloy nanowires, the structural change from hcp to fcc was accompanied by a change of the FORC distribution shape, where it became more symmetric [8]. Therefore, to describe the changes within the FORC investigation of the Ni55Fe43Ga2 nanowires, a detailed analysis of the obtained results is necessary. We have shown that the Ni55Fe43Ga2 nanowires show a magnetic shape memory behaviour. The magnetization increase within the isothermal measurement is temperature- and magnetic field dependent. The diverging FORC distribution shows that the nanowires array behaves as a multi-domain and highly interacting system and the vertical spread of the divergence narrows with respect to the Hc axis of the FORC density contour plot. To determine the origin of the FORC distribution change at different temperatures, further analysis of the FORC measurements is necessary. However, the current results show that the Ni55Fe43Ga2 nanowires show an elongation within the low-temperature measurements, below the transformation temperature region that was determined during the isothermal magnetization measurements. Acknowledgement: This work was supported by Slovak Grant Agency VEGA 1/0053/19, Slovak Grant Agency grant number APVV-16-0079, VVGS-2019-1231 and VVGS-PF-2020-1420.

**References:**

[1] Y. Li, D. Zhao, and J. Liu, Sci. Rep., vol. 6, pp. 1–11 (2016) [2] M. Hennel, L. Galdun, T. Ryba, J. Magn. Magn. Mater., vol. 511, p. 166973 (2020) [3] P. Cejpek et al., J. Alloys Compd., vol. 775, pp. 533–541 (2019) [4] B. Hernando et al., Appl. Phys. Lett., vol. 92, pp. 12–14 (2008) [5] C. R. Pike, et al., Phys. Earth Planet. Inter., vol. 126, pp. 11–25 (2001) [6] A. R. Muxworthy, A. P. Roberts, Encycl. Geomagn. Paleomagn., pp. 266–272 (2007) [7] A. P. Roberts, D. Heslop, X. Zhao, Rev. Geophys., vol. 52, pp. 557–602 (2014) [8] A. S. Samardak et al., J. Alloys Compd., vol. 732, pp. 683–693 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/13d044c3864a26387342bf9f3f7b6fe9.jpg)
Fig. 1: Isothermal magnetization measurements at different temperatures

![](https://assets.underline.io/uploads/markdown_image/1/image/cf8ea57120a09f5c7343b6d90adee253.png)
Fig. 2: FORC density distribution of the Ni55Fe43Ga2 nanowires at different temperatures

 Temperature-dependent FORC Investigation of Electrodeposited Magnetic Shape Memory Nanowires Array

The study of 1D-nanostructures has been intensified in the last few decades due to the development of fabrication methods of metallic, semiconductors and insulator materials aiming applications in several areas [1]. In particular, multi-segmented magnetic nanowire (NW) arrays are prospective candidates for an extensive range of applications such as racetrack memory devices, spintronic, and drug delivery [1, 2, 3]. These possibilities are due to the number of degrees of freedom related to the intrinsic shape anisotropy combined with the potential to introduce different materials along the NW’s length. Concerning practical applications, understanding the role of layers with distinct structural and magnetic properties can be a path to avoid some issues such as system overheating and Walker breakdown in racetrack devices. For instance, micromagnetic simulations revealed that the combination of Co segments with different structures, bcc and hcp, promotes a faster way of writing information in 3D racetrack memory devices [2]. This observation results from the high magnetocrystalline anisotropy along the wire length induced by the Co-hcp structure. Although these evaluations seem promising, thorough experimental research of multi-segmented NWs with low and high anisotropy components still needs to be performed. Here, we present the FeCo layer properties’ evaluation onto multi-segmented NW arrays produced through DC electrodeposition into ordered porous alumina templates with 40 nm of pore diameter and 60 µm of length. For each layer’s deposition, a Pt electrode was used as the counter electrode, Ag/AgCl as the reference electrode, and an Au layer as the working electrode [5]. Two samples were prepared: 1) Au [200 nm] / Fe33Co67 [24 µm] / Au [10 nm] and 2) Au [200 nm] / Ni90Cu10 [1 µm] / (Fe33Co67 [13 µm] / Au [10 nm])x3, where the indicated length was obtained from scanning electron microscopy (SEM) images and the alloy’s stoichiometry from energy dispersive spectroscopy (EDS). X-ray diffraction (XRD) measurements at room temperature revealed the formation of bcc structure of FeCo with the (110) preferential orientation for both samples and an additional hcp phase with the (110) preferential orientation for FeCo tri-segmented NWs (Figure 1). The magnetic hysteresis loops acquired at room temperature for the Au/FeCo/Au arrays present the easy magnetization axis along the parallel direction, evidencing a typical strong shape anisotropy [5]. Distinctly, when three FeCo segments of 13 µm are deposited along the NW’s length, the arrays present an isotropic magnetic behavior with an increase of the coercive field when applying the magnetic field perpendicular to the nanowires’ axis (Figure 2). This change in magnetic behavior for the segmented NWs might be related to the presence of an hcp phase that induces a perpendicular magnetocrystalline anisotropy. However, further research should be performed to better comprehend the interplay between the NiCu and FeCo layers into the NW arrays. In summary, multi-segmented NWs of FeCo alloys were successfully achieved through the electrodeposition process into porous templates. The growth of FeCo segments leads to the formation of hcp structures and the observation of an isotropic magnetic behavior. This can be related not only to the structural properties but also to the interplay between FeCo segments along the NW’s length. A more complete evaluation of the magnetic properties of the produced samples should be performed to fully understand the role of the different layers in the magnetocrystalline anisotropy of the arrays. This work was financially supported by projects POCI-01-0145-FEDER-028676 and UIDB/04968/2020 from Portuguese FCT and COMPETE 2020 (FEDER) and IF/01159/2015, POCI-01-0145-FEDER-031302/PTDC/FIS-MAC/31302/2017. .

**References:**

References:: [1] C. T. Sousa et al., Appl. Phys. Rev., vol.1 , p. 031102 (2014); [2] J. Rial and M. P. Proenca, Nanomaterials, vol. 10, p. 2403 (2020); [3] D. Wang et al., Materials, vol. 12, p. 3908 (2019); [4] C. Bran et al., J. Phys. D: Appl. Phys., vol. 48, p. 145304 (2015); [5] E. M. Palmero et al., Nano Research, vol. 12, p. 1547 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/419fc130f5d8af612615b50ad0e953e0.jpg)
Figure 1: XRD patterns for Au/FeCo/Au and Au/NiCu/[FeCo/Au]3 segmented nanowires with the Bragg peak positions for bcc (green) and hcp (red) structures.

![](https://assets.underline.io/uploads/markdown_image/1/image/59bc97224bca21ea1066106778e1c21d.jpg)
Figure 2: Hysteresis loops obtained by applying the magnetic field perpendicular to the NWs’ length

 Isotropic magnetic behavior of multi-segmented FeCo nanowire arrays

Striving for create ultrafast electronics led to the development of three-dimensional compact architectures in many disciplines including magnetism. Coercivity, squareness, and magnetic anisotropy can be tailored by varying the geometry and/or spatial distribution of the magnetic functional units [1, 2]. Elongated elements (nanowires and nanotubes) have been used in the number of technologies. The problems concerned with the complicated dipole-dipole interactions in arrays of such elements motivates in researching new designs for these elements. Two-phase nanowires with a coaxially combined or varied along axis phases could generate additional applied advances. In this work, we describe experimental results concerning the bi-segmented and coaxial Co/Ni rods in porous of track etched polycarbonate membranes (PCTE) and focus on the comparison of their magnetic properties. The 3D coaxial nanostructures investigated consist of a cylindrical cobalt core that is completely surrounded by a shell of nickel layer. The bi-segmented (BS) rods contain two coupled rods of nickel and cobalt. The magnetic anisotropy of the bi-segmented and core-shell rods electroless deposited to the pores of PCTE was studied. The Co and Ni deposition into the PCTE membranes pores is carried out by electroless reduction of metal-salt solution with sodium hypophosphite as reducing agent. In a first step in the case of coaxial rods, the inner pore walls were treated with paladium chloride used as a nucleating agent. In the next step the pores are coated with nickel by electroless deposition. The deposited Ni tubes are shown in Fig.1a. Then the Ni tubes were filled with cobalt by electroless deposition. The coaxial rods are shown in Fig. 1b. The cobalt core has a diameter of about 200 nm, which is determined by the PCTE pore diameter and the thickness of the Ni shell layers. The reference tube and rod samples consisting of ‘‘shell only’’ or ‘‘core only’’ was prepared using the same technique. For the synthesis of bi-segmented rods one side of the membrane was coated by a thin layer of thermal-sputtered cooper to create an electrochemical potential that promotes the metal deposition inside PCTE channels along the pore axis. Then Co/Ni rods (along-axis) were prepared by electroless deposition. The employed rods growth method allows for tuning both the composition and crystalline structure of each individual Co and Ni segments. The magnetic properties and structure of the rods are characterized by scanning electron microscopy, X-ray diffraction, ferromagnetic resonance (FMR) and vibrating sample magnetometer. Information on local magnetic anisotropy is obtained using the approach to magnetic saturation curves. The X-ray powder diffraction shows that the Ni and Co alloys for the rods of the both types were crystalline with fcc structure. The local magnetic anisotropy field of Co/Ni rods was estimated to be in the range from 0.9 to 2 kOe. The core/shell geometry of Co@Ni rods transpires in their physical properties. A staggering difference is observed between the FMR spectra measured on arrays of Co/Ni core/shell rods, Co/Ni BS rods and the ‘‘parent’’ samples, namely, Ni tubes without core and Co rods without Ni shell (fig.2). The FMR spectrum for Co core and Ni tube consists of a single absorption line. For Co/Ni and Co@Ni rods the FMR spectrum consists of two wide absorption lines corresponding to different layers. The presence of graded Co or Ni content at layer boundaries could give rise to graded anisotropy effects (that is, local variations of the effective magnetic anisotropy along the rod axis). Such variations in magnetic anisotropy could manifest in variations of resonance fields for different rod segments and could increase FMR linewidth. The measurements of FMR spectrum and magnetization curves at different orientations of an external field allow us to obtained data about macroscopic magnetic anisotropy of synthesized rods. It was found that for Co rods easy magnetization axis lying along the long axis of the rod, and its value is close to magnetic shape anisotropy of elongated column pMs. The overall magnetic anisotropy of the array is mainly determined by the following three contributions: the anisotropy results from the shape effect of the individual rods , which will induce a magnetic easy axis parallel to the wire axis; magnetostatic coupling among the rods, which tends to develop a magnetic easy axis perpendicular to the rod axis; and the local anisotropy field, which consists of magnetocrystalline anisotropy and anisotropy of intrinsic strain. In the case of BS rods for distribution density of rods more than 20% the contribution from dipole-dipole interaction was comparable to those for shape anisotropy. The room temperature magnetic behavior of the core-shell Co/Ni nanorod arrays is also studied and correlated with their structural and morphological properties. The successful synthesis of the bi-segmented rods with coaxial (Co@Ni) and along-axis (Co/Ni) segmentation was demonstrated. The magnetic anisotropy field, ferromagnetic resonance field, linewidth and the coercivity are mainly determined by the artificially created interface boundaries for two types of bi-segmented rods with coaxial (Co@Ni) and along-axis (Co/Ni) segmentation. This work was funded by the RFBR, the Government of the Krasnoyarsk Territory, the KRFS (project no. 20-43-240003)

**References:**

1. R. Streubel, J. Lee, D. Makarov et al, J. Phys. D, 49, 363001, (2016) 2. E. Y. Vedmedenko, R. K. Kawakami, D. D. Sheka et al., J. Phys. D. Appl. Phys. 53, 453001 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/522d7e8b1522ae40fd8dc8d80470c462.jpg)
Fig.1 SEM image of Ni tube (a) and Co@Ni core/shell rods (b).

![](https://assets.underline.io/uploads/markdown_image/1/image/646e08d194d1a030767c7cfdcace80d9.jpg)
Fig.2 a - FMR spectra for Co/Ni core-shell rods (1) and BS rods (2); b- Co rods (1), Ni tubes (2).

 Core-shell and Bi-segmented Cobalt-Nickel Nanorods Prepared by Electroless Deposition

Properties of two-dimensional spatially periodic nanostructures formed by a corrugated 2D structured as substrate which covered by gold and Ce:YIG films were studied by magneto-optical spectroscopy techniques. It was shown that the structures exhibit a considerable magneto optical response to longitudinal Kerr effect at wavelength of 450 nm and this enhancement seems to be related to excitation of localized surface plasmon-polaritons(LSPR) in the array of nanorods created in this structure. Recent achievements in photonics and optoelectronic require the advanced magneto-photonic microdevice with ability of control the magneto-optical response in micron and submicron scales. The Advanced magneto-optical devices tend to miniature the components, which requires strong magneto-optical effect in small scale. Combination of magnetic and plasmonic materials with different functionalities into a magneto-plasmonic structure is considered as a promising route to enhance the magneto-optical activity [1]. On the one hand, plasmonics allows for extreme electromagnetic field enhancement and subwavelength localization. On the other hand, MO materials bring optical non-reciprocity properties in the presence of magnetic field. Early studies on magneto-plasmonic structures addressed propagating surface plasmon-polariton (SPP) along the smooth surface of a metallic film [2]. In parallel to the studies on SPPs, the rapid developments in nanofabrication, enable extending studies of optics in nanoscale with nanostructures also supporting localized surface plasmon (LSPR) [3,4]. In the recent work, we investigate the magneto-optical response of a 2D magnetoplasmonic nanostructure which can support LSPR. A two-dimensional 2D magneto-plasmonic nanostructure was prepared by nanoimprint lithography method. For this purpose, a 2D charge coupled device (CCD) separated from a camera was used as stamp and the poly-dimethylsiloxane (PDMS) substrate was patterned as 2D substrate. First, the substrate was covered by gold layer of 30 nm thickness as plasmonic material by using a PVD coating device. Then it was coated by a Ce:YIG layer with an approximate thickness about 100 nm as magnetic material by using of pulsed laser deposition method. Actually this structure composed of 2D array of cubic holes with width and length of 3 µm and depth of 500 nm. these cubic holes were arranged in 2D with a distance about 170 nm. The Schematic of this structure is shown in Fig. 1a. Also, the periodicity of the sample and its surface has been examined by scanning electron microscopy (SEM) and shown in Fig. 1b. The nanometric distance between holes well creates nanorods which can support LSPR in the structure and this surface lattice resonance. Investigation of MO activity of the prepaid sample was carried out by a home-made longitudinal spectral Kerr effect set up with applying a DC magnetic field in the plan of sample and parallel to the incidence plane. The linear polarized light was incident on the sample at incidence angle of 30°. In our set up, the linear poliarized light was achieved by passing the unpolarized broadband light from a polaroid sheet which can linearly polarized the light in the wavelength range of 400-700 nm. Thereafter, the reflected spectra of the sample were recorded for positive and negative directions of magnetic field in rotational analyzer method. Finally, the recorded spectra were analyzed by a Labview program. The longitudinal Kerr effect spectrum showed a sharp peak at the wavelength of 450 nm which is related to Ce:YIG magneto-optical response.

**References:**

[1] Maccaferri, N., Zubritskaya, I., Razdolski, I., Chioar, I. A., Belotelov, V., Kapaklis, V., & Dmitriev, A. 2020. J. Appl. Phys,127, 8, 080903. [2] D. Martin-Becerra, J.B. Gonzalez-Díaz, V.V. Temnov, A. Cebollada, G. Armelles, T. Thomay, A. Garcia-Martín and M. Ujue Gonzalez, 2010, Appl. Phys. Lett. 97, 183114. [3] V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, Achanta Venu Gopal, D. R. Yakovlev, A. K. Zvezdin, M. Bayer (2011), Nature Nanotechnol, 6, 370. [4] B. Sepúlveda, J. B. Gonzalez-Díaz, A. Garcia-Martín, L. M. Lechuga, and G. Armelles, 2010, Phys. Rev. Lett. 104, 147401.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a2bf0ac2c504a3ad8ec1b3e56b5fa519.jpg)
Fig1. (a) schematic of 2D magneto-plasmonic structure composed of PDMS corrugated substrate covered by gold layer with thickness of 30 nm and Ce:YIG layer with approximate thickness of 100 nm. (b) SEM image of prepaid magneto-plasmonic structure.

![](https://assets.underline.io/uploads/markdown_image/1/image/63662f9edd1974d5d788347bf635aa74.jpg)
Fig.2: MO spectrum of the 2D grating sample composed of Gold and Ce:YIG layer measured at incident angle of 30° by home-made spectral longitudinal Kerr set up.

 Unexpected Longitudinal Kerr rotation in two dimensional magneto plasmonic structure

Amorphous glass-coated microwires are among the excellent material that can be used in sensor and spintronic devices. The magnetization process is realized due to the fast domain wall propagation. The studies on domain wall dynamics showed that additional perpendicular magnetic field changes domain wall velocity [1, 2]. Moreover, after the rotation of the microwire in the perpendicular magnetic field the difference in the domain wall velocity is even more significant [3]. However, the obtained results are contrary to the expectations based on previous knowledge. Due to the cylindrical shape of the wires, no change in domain wall velocity was expected for different rotations. The results are explained in terms of the gradient of the perpendicular magnetic anisotropy in the cross-section of the wire. The gradient is induced to the microwire during the fabrication process. The water stream causes additional induced stresses due to the cooling of the microwire from one side (Fig. 1a). The direct observation of such stresses in the cross-section of the wire is not possible due to the amorphous structure of the microwires. However, it is clearly visible when the sample is annealed above the crystallization temperature (Fig. 1b). In this work, we present the domain wall (DW) dynamics studies on the sample (Fe76Si9B10P5) as-cast and annealed below the crystallization temperature (at 450 °C) (Fig. 2). The DW velocity v is described by the following relation [4]: v = S(H - H0) (1) where S is DW mobility, and H0 critical magnetic field. The DW velocity of the as cast sample is linearly increasing for different angles of rotation θ (Fig.2a). For θ = 180°, DW velocity increases up to 350 A/m with mobility S = 1.44 m2s-1A-1. From 350 A/m, the DW mobility is S = 24.9 m2s-1A-1. However, after annealing, the DW motion is observed from Haxial = 550 A/m with the mobility S = 1.73 m2s-1A-1 up to 700 A/m (Fig.2b). DW mobility from Haxial = 700 A/m is incomparably smaller in comparison to the case before annealing, with the value S = 6.79 m2s-1A-1. When the sample is annealed, it leads to the release of the stresses induced in the cross-section of the microwire. Annealing causes the homogenization of the sample, and as a result, a significant decrease in DW mobility is observed. Thus, an effective mechanism for suppressing the angular dependence of DW mobility in a perpendicular magnetic field is annealing under suitable conditions. Acknowledgements: This work was supported by Slovak Grant Agency VEGA 1/0053/19, VEGA 1/0195/17; Slovak Grant Agency grant number APVV-16-0079, APVV-17-0184, APVV SK-FR-2017-024 and Pavol Jozef Šafárik University internal grant system VVGS-2016-320.

**References:**

[1] R. Varga et al., Physica Status Solidi A, Vol. 213, p. 356–362 (2016). [2] K. Richter et al., Applied Physics Letters, Vol. 96, 182507 (2010). [3] L. Fecova, K. Richter, and R. Varga, Acta Physica Polonica A, Vol. 137 (5), p. 849-851 (2020). [4] V. Zhukova et.al, Journal of Applied Physics, Vol. 111, 07E311-1 (2012).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/70d8ab1607609771a6973e4fac77b8eb.jpg)
Fig.1 Taylor-Ulitovski method of drawing the glass-coated microwire Fe76Si9B10P5, which is quenched by the water jet from one side in order to obtain the amorphous structure (a), and the stress distribution in the section of the amorphous wire annealed above crystallization temperature (b).

![](https://assets.underline.io/uploads/markdown_image/1/image/d4ca30e3a4acdb9987c890d60d17e064.png)
Fig.2 Domain wall velocity as a function of the axial magnetic field in the perpendicular magnetic field for the as-cast sample (a) and sample annealed below the crystallization temperature (b).

 The annealing effect on domain wall dynamics in wires with induced gradient of the perpendicular anisotropy

Introduction Modern magnetic material applications require homogeneous microstructures consisting of monodisperse magnetic entities. A facile route towards such microstructures is to exploit other materials as templates of model nanostructures via a “bottom-up”, low-cost approach. To that end, monodisperse nanosphere single-layers which tend to form 2D-hexagonal close packed patterns can be utilized either as templates for the deposition of “nanocaps” or as masks for the formation of triangular-like islands [1]. Although a lot of work has been devoted to the optimization these arrays [2,3] little progress has been made towards the use of self-assembly magnetic materials [4–7]. Here, we explore the effect of in-plane and perpendicular magnetic fields on the spatial arrangement of superparamagnetic nanoparticles. Thus, we add the long range magnetic dipolar interactions to the competing nanoparticle-surface (substrate hydrophobicity-hydrophilicity) and the nearest neighbor nanoparticle-nanoparticle interactions which control order and agglomeration. We present the optimization of the self-assembly of paramagnetic polystyrene nanospheres (0.25 nm - 1.43 nm) obtained by spin coating and drop casting, with respect to monolayer formation, substrate coverage, 2D hexagonal packing, and size of ordered areas. Arrays prepared under zero field by drop casting and spin coating were compared with those obtained under the effect of an in plane or perpendicular magnetic field. Experimental Methods - Results We utilize PS nanospheres with different sizes (0.270μm, 0.536μm and 1.43μm) which incorporate superparamagnetic Fe3O4 nanoparticles. Thermally oxidized silicon wafers, with approximately 500nm oxidation layer, are used as substrates. Prior to the deposition, the substrate’s hydrophilicity is improved using piranha solution. Contact angle measurements were performed to determine the hydrophilicity of the substrates, before and after the surface treatment. After the surface treatment, contact angle was measured as low as 9.3deg compared to 46deg of the untreated wafer. The different methods utilized are summarized in Table 1. In the drop casting experiments droplets of an aqueous suspension were mixed with tritonX – 100 and methanol (1:400) were deposited on the hydrophilic surface. A small electromagnet was used to generate the magnetic field. This method has two main geometrical control parameters, substrate inclination and angle of the applied magnetic field. In spin coating experiments under perpendicular field the surface-treated substrate is rotated on the platform of the spin coater which is placed in the middle of a coil. For in-plane field application, the sample is rotated until the solution expands on the surface; then it is removed from the spin coater and left to settle under the field on horizontal platform inside a coil. As surface wettability is an important parameter, two different surfactants have been employed and the results are compared. For the tritonX-100 treated samples rotation speeds up to 8000 rpm with a standard acceleration rate of 200rpm/s were used. For the SDS treated samples experiments, lower rotation speeds up to 800 rpm are optimal. For the observation of the macroscopic and microscopic surface morphologies of the samples, we used a Zeiss AxioImager A1 optical microscope fitted with a Canon 80D DSLR and a Scanning Electron Microscope (SEM, JEOL Ltd). During spin coating, competing forces like gravity, centrifugal, magnetic dipolar interactions and surface tension have a significant impact on the NPs self-assembly. Without magnetic fields the arrays can be optimized for monolayer formation, substrate coverage, 2D hexagonal packing, and size of ordered areas. The use of in-plane magnetic fields permits the organization of NPs in directional arrays along the direction of the field. Perpendicular fields tend to create 3D structures in competition to the hydrophilicity of the substrates. Acknowledgement: This research is co-financed by Greece and the European Union (European Social Fund- ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning 2014-2020» in the context of the project “Dynamic Response of Magnetically organized nanoelements (DAMON) (MIS5047646).

**References:**

[1] T.C. Ulbrich, D. Assmann, M. Albrecht, Magnetic properties of Co/Pt multilayers on self-assembled particle arrays, J. Appl. Phys. 104 (2008) 084311. https://doi.org/10.1063/1.3003064. [2] A. Chandramohan, N. V. Sibirev, V.G. Dubrovskii, M.C. Petty, A.J. Gallant, D.A. Zeze, Model for large-Area monolayer coverage of polystyrene nanospheres by spin coating, Sci. Rep. 7 (2017) 9–11. https://doi.org/10.1038/srep40888. [3] B. Park, S.Y. Na, I.-G. Bae, Uniform two-dimensional crystals of polystyrene nanospheres fabricated by a surfactant-assisted spin-coating method with polyoxyethylene tridecyl ether, Sci. Rep. 9 (2019) 11453. https://doi.org/10.1038/s41598-019-47990-z. [4] J.D. Feldmann, G.J. Kalman, P. Hartmann, M. Rosenberg, Ground state of magnetic dipoles on a two-dimensional lattice: Structural phases in complex plasmas, Phys. Rev. Lett. 100 (2008) 085001. https://doi.org/10.1103/PhysRevLett.100.085001. [5] V. Håkonsen, G. Singh, P.S. Normile, J.A. De Toro, E. Wahlström, J. He, Z. Zhang, Magnetically Enhanced Mechanical Stability and Super -Size Effects in Self-Assembled Superstructures of Nanocubes, Adv. Funct. Mater. 29 (2019) 1904825. https://doi.org/10.1002/adfm.201904825. [6] C. Jiang, Synthesis , Assembly , and Integration of Magnetic Nanoparticles for Nanoparticle-Based Spintronic Devices, Tesis. (2018). https://doi.org/10.13140/RG.2.2.17523.22563. [7] M. Hu, H.-J. Butt, K. Landfester, M.B. Bannwarth, S. Wooh, H. Thérien-Aubin, Shaping the Assembly of Superparamagnetic Nanoparticles, ACS Nano. 13 (2019) 3015–3022. https://doi.org/10.1021/acsnano.8b07783

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b380468d75bdd830a6c866b7024bdd5a.jpg)
Figure 1 - Optical microscopy image of 1,43μm superparamagnetic PS spheres deposited on a tritonX-100 treated surface, under an in-plane magnetic field.

![](https://assets.underline.io/uploads/markdown_image/1/image/79f88e3ce121f13fbf4151fb1a01c33f.jpg)
Table 1 - Methods utilized for drop casting and spin coating experiments

 Superparamagnetic nanosphere arrays: Self-assembly and the effect of applied magnetic fields.

Superparamagnetic Iron Oxide Nanoparticles (SPION) are nanosize beads of iron oxides. Their peculiar magnetic behaviour makes them particularly suited for a variety of biomedical applications, ranging from cellular imaging to cancer treatment by hyperthermia. The usual theory used to describe their magnetic behaviour is that developed by Paul Langevin [1], which only applies to idealized (isotropic, monodisperse in size and non-interacting) nanoparticles at high temperatures. Reality however usually deviates from that theoretical framework. First, real samples are polydisperse in size, which impacts the particles' magnetic moments and therefore their behaviour. Second, particles usually have at least one easy magnetization axis, which adds a term to their Hamiltonian. Finally, particulary in biological media, they tend to aggregate, leading to locally high particle volumic fractions and therefore dipolar interaction between their magnetic moments [2]. Moreover, as demonstrated by Néel and Brown [3], at low temperatures the particles’ magnetic moments and anisotropy axises appear effectively blocked at their initial directions. Under the Néel blocking temperature, the particles are unable to reorganize their internal moments to change the resulting moment's direction, and under the Brown blocking temperature they are unable to rotate so as to align their easy axis with their moment and/or the external field. All those phenomena impact the magnetization of particle ensembles in a non-trivial way and are impossible to study simultaneously theoretically. In this work, these deviations from the Langevin law are studied numerically, at thermodynamic equilibrium, using a Metropolis algorithm, and compared with experimental data obtained on a Vibrating Sample Magnetometer. The Metropolis algorithm is adapted to take into account the Néel and Brown blocking of the particles, as those time-dependant effects are not explained by free energy minimization. Its Hamiltonian is also chosen to take into account the particles' magnetic anisotropy and the dipolar interactions between the particles as well as the interaction of their moments with the magnetic field. Thorough tests were led on the simulation program to ensure correct convergence of the algorithm. Notably, the temperature step used in the ZFC curve does not impact the simulation results, as expected from a robust computation. Convergence was tested with respect to all of the simulation parameters, and the impact of the magnetic anisotropy on the MH curves was validated by comparing to previous theoretical results obtained by M. Respaud et al [4]. Various other validation tests were conducted. The interest of using numerical simulation is that it allows to discriminate the effects of each tweak to the theory, leading to a better understanding of their various impacts. Curves studying the effect of varying each parameter were obtained, as can be seen in figure 1, where the effect of the magnetic anisotropy on the MH curve is compared in different situations. The ultimate goal being to replicate by numerical simulation the experimental results, it is important to understand how each effect impacts the shape of the curves, to have a clear sense of which experimental parameters impact the results and which don't. In terms of experimental data, two types of magnetization curves in particular are obtained: so called MH curves, where the magnetization is plotted versus the external magnetic field that is applied, and magnetization vs temperature curves. These can be obtained following different protocols, leading to different types of curves, the most common being the zero field cooled (ZFC) curve and the field cooled (FC) curve. Their shape is, naturally, impacted by the different effects at play, and by the precise experimental protocol, as can be seen in figure 2, where a ZFC curve is compared with two FC curves: one obtained after freezing the sample under no magnetic field and one after freezing it under a 5 mT magnetic field. FC/ZFC curves and MH curves (at various temperatures) of three different particle samples were obtained and compared. In particular, PolyMAG particles, which are commercialized for transfection protocols, were studied, and revealed a very unusual ZFC curve, showing no peak nor the usual bell shape of those graphs. One of the future goals of the numerical simulation will be to explain, at least qualitatively, this peculiar behaviour.

**References:**

[1] P. Langevin, J. Phys. Theor. Appl., Vol. 4 (1), p. 678, (1905) [2] M. Lévy, C. Wilhelm, et al., Nanoscale, Vol. 3, p. 4402 (2011) [3] W.F. Brown, Jr, Physical Review, Vol. 130(5), p. 1677 (1963) [4] M. Respaud, J. App. Phy., Vol. 86, p. 556 (1999)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/debde9c1e8e3d098529f51c4e4fed9ce.jpg)
Simulated MH curve of the system in different cases : without considering magnetic anisotropy, and considering magnetic anisotropy with various dispositions of the particles' anisotropy axises ; aligned with the external field (θ = 0), perpendicular to it (θ = 90°) or randomly oriented ("distributed" case).

![](https://assets.underline.io/uploads/markdown_image/1/image/a3934a84a7017a45325a9cf929652605.jpg)
Experimental ZFC and FC curves of a 6nm sample under different freezing protocols: freezing the sample under 0T to 2K (ZFC), freezing it under 5mT to 2K, and freezing it under 5mT to 175K and then under 0T to 2K.

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