France



Achieving new possibilities of cell manipulation or of other microbiological species is one of the most important tasks of the latest lab-on-a-chip devices [1-3]. High throughput and precise movement control are the figures of merit for new tools or chip designs. Common concepts consist of labeling biological cells or other biological entities with magnetic nanoparticles to achieve transport by timely and spatially varying magnetic field gradients [4]. In this context, superparamagnetic microbeads (MB) are widely used to imitate the properties of tagged cells or act as carriers for smaller biological species like DNA-strings or proteins. The particles or MBs can be manipulated on top of hard magnets [5] or soft magnetic thin film structures [6]. Recent research has shown many differently designed patterned thin film structures, featuring multiple advantages for the transport of MBs.&lt;br/&gt;One of the transport concepts relies on the interaction of their magnetic moment with a stray magnetic field gradient of arranged soft-magnetic thin film elements. Magnetic field sequences create varying potential states, enabling specific MB trajectories. In narrow soft magnetic tracks, magnetic microstructures that exhibit strong local stray field gradients are moved to drag the MBs along certain directions. For example, two-dimensional arrays of soft magnetic elements with various magnetization states varying with applied magnetic fields enable complex MB manipulation [2]. In every case, the maximum speed of the MB is limited by the hydrodynamic drag force, the surface friction, and by the magnetic force. This links the magnetic moments of the thin film elements and the MB, the friction coefficients, and the MB size.&lt;br/&gt;Beneficial and applicable unidirectional movement of a MB and a magnetically labeled rat embryonic fibroblast cell is demonstrated. We show the unidirectional transport of MBs and cells independent of the sign of the magnetic stimuli. Oval shaped elements made from a soft magnetic amorphous iron-based alloy are arranged in a one-dimensional chain, allowing MB transport whether clockwise or counter-clockwise in-plane rotating magnetic fields are applied. A directional motion scheme is achieved by exploiting the stray field dependence of the curvature radius of the facing magnetic elements.&lt;br/&gt;Three dimensional simulations [7] are used to forecast the motion of a particle along a chain of ovals and provide the theoretical background to the experimental results. Magnetic potential energy landscapes are calculated between the MB anticipated as magnetic dipoles and the micromagnetic structure of the oval elements simulated using mumax&lt;sup&gt;3&lt;/sup&gt; [8]. We find that an overlap of the potential minima of two neighboring elements for a spacing similar to the diameter of the MB enables a handover of MBs between magnetic elements. The agreement between the numerical simulated bead trajectories and the experimental movement path is shown in Fig. 1. The unidirectional motion scheme of the beads is demonstrated for different starting conditions for clockwise and counterclockwise rotating fields. The motion is independent of the sense of field rotation. The same manipulation options are obtained with a MB engulfed rat embryonic fibroblast cell as shown in Fig. 2.&lt;br/&gt;The robust diode-like particle guidance along predefined tracks, formed by chains of elements, holds also great potential for lab-on-a-chip applications, including cell sorting or highly controllable manipulation of biological carriers. The diode-like behavior of the oval elements leaves the direction of magnetic field rotation as a degree of freedom unexploited, permitting its usage for adding-on other application relevant manipulation schemes. Various aspects and options of the motion rectifying magnetic structures will be discussed.&lt;br/&gt;&lt;br/&gt;J.M., F.B., and U.S. acknowledge funding through the Deutsche Forschungsgemeinschaft grants DFG MC 9/13-1 and MC 9/13-2. C.A. and C.S. thank the Volkswagen Foundation for funding the project &quot;Molecularly controlled, stimuli-sensitive hydrogels for dynamically adjustable biohybrid actuators&quot;. S.S. and C.S. acknowledge funding of the Research Training Group RTG 2154 &quot;Material for Brain&quot; through the Deutsche Forschungsgemeinschaft. J.M. thanks S. Gutekunst for stimulating discussions. The authors thank L. Thormählen for magnetic thin film deposition.

**References:**

[1] S. Rampini, P. Li, and G. U. Lee, Lab Chip 16, 3645-3663 (2016).&lt;br/&gt;[2] U. Sajjad, E. Lage, and J. McCord, Adv. Mat. Int. 5, 1801201 (2018).&lt;br/&gt;[3] B. Lim, P. Vavassori, R. Sooryakumar, et al., J. Phys. D: Appl. Phys. 50, (2016).&lt;br/&gt;[4] T. Henighan, A. Chen, G. Vieira, et al., Biophys. Jour. 98, 412-417 (2010).&lt;br/&gt;[5] J. Pivetal, D. Royet, G. Ciuta, et al., J. Magn. Magn. Mat. 380, 72-77 (2015).&lt;br/&gt;[6] U. Sajjad, R. B. Holländer, F. Klingbeil, et al., J. Phys. D: Appl. Phys. 50, (2017).&lt;br/&gt;[7] F. Klingbeil, F. Block, U. Sajjad, et al., Sci. Rep. 10, 1-12 (2020).&lt;br/&gt;[8] A. Vansteenkiste, J. Leliaert, M. Dvornik, et al., AIP Adv. 4, 107133 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/515b7a81ae7380b50d0574aff749114e.jpg)
Fig. 1: Simulation data of a single MB motion for clockwise magnetic field rotation. Snapshots of the unidirectional motion together with the corresponding potential landscape are shown for four magnetic field angles. The corresponding matching experimental behavior for the same parameters are shown. The calculations and experiments were performed at clockwise rotating magnetic fields of 40 mT with a rotation frequency of 1.0 Hz.

![](https://assets.underline.io/uploads/markdown_image/1/image/c9bccb77854ad0f52c7d5fc0767f13c4.jpg)
Fig. 2: Forward transport of a microbead engulfed by a rat embryonic fibroblast cell. The initial position of the cell and the microbead on the upper side of an oval structure is marked, demonstrating a forward motion even under the condition of a starting velocity in the backward direction. Here a counterclockwise rotating magnetic field of 40 mT with a rotation frequency of 0.3 Hz is applied.

INTERMAG 2021

 Unidirectional Transport of Superparamagnetic Beads and Biological Cells along an Oval Shaped Magnetic Element Path

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Achieving new possibilities of cell manipulation or of other microbiological species is one of the most important tasks of the latest lab-on-a-chip devices [1-3]. High throughput and precise movement control are the figures of merit for new tools or chip designs. Common concepts consist of labeling biological cells or other biological entities with magnetic nanoparticles to achieve transport by timely and spatially varying magnetic field gradients [4]. In this context, superparamagnetic microbeads (MB) are widely used to imitate the properties of tagged cells or act as carriers for smaller biological species like DNA-strings or proteins. The particles or MBs can be manipulated on top of hard magnets [5] or soft magnetic thin film structures [6]. Recent research has shown many differently designed patterned thin film structures, featuring multiple advantages for the transport of MBs. One of the transport concepts relies on the interaction of their magnetic moment with a stray magnetic field gradient of arranged soft-magnetic thin film elements. Magnetic field sequences create varying potential states, enabling specific MB trajectories. In narrow soft magnetic tracks, magnetic microstructures that exhibit strong local stray field gradients are moved to drag the MBs along certain directions. For example, two-dimensional arrays of soft magnetic elements with various magnetization states varying with applied magnetic fields enable complex MB manipulation [2]. In every case, the maximum speed of the MB is limited by the hydrodynamic drag force, the surface friction, and by the magnetic force. This links the magnetic moments of the thin film elements and the MB, the friction coefficients, and the MB size. Beneficial and applicable unidirectional movement of a MB and a magnetically labeled rat embryonic fibroblast cell is demonstrated. We show the unidirectional transport of MBs and cells independent of the sign of the magnetic stimuli. Oval shaped elements made from a soft magnetic amorphous iron-based alloy are arranged in a one-dimensional chain, allowing MB transport whether clockwise or counter-clockwise in-plane rotating magnetic fields are applied. A directional motion scheme is achieved by exploiting the stray field dependence of the curvature radius of the facing magnetic elements. Three dimensional simulations [7] are used to forecast the motion of a particle along a chain of ovals and provide the theoretical background to the experimental results. Magnetic potential energy landscapes are calculated between the MB anticipated as magnetic dipoles and the micromagnetic structure of the oval elements simulated using mumax3 [8]. We find that an overlap of the potential minima of two neighboring elements for a spacing similar to the diameter of the MB enables a handover of MBs between magnetic elements. The agreement between the numerical simulated bead trajectories and the experimental movement path is shown in Fig. 1. The unidirectional motion scheme of the beads is demonstrated for different starting conditions for clockwise and counterclockwise rotating fields. The motion is independent of the sense of field rotation. The same manipulation options are obtained with a MB engulfed rat embryonic fibroblast cell as shown in Fig. 2. The robust diode-like particle guidance along predefined tracks, formed by chains of elements, holds also great potential for lab-on-a-chip applications, including cell sorting or highly controllable manipulation of biological carriers. The diode-like behavior of the oval elements leaves the direction of magnetic field rotation as a degree of freedom unexploited, permitting its usage for adding-on other application relevant manipulation schemes. Various aspects and options of the motion rectifying magnetic structures will be discussed. J.M., F.B., and U.S. acknowledge funding through the Deutsche Forschungsgemeinschaft grants DFG MC 9/13-1 and MC 9/13-2. C.A. and C.S. thank the Volkswagen Foundation for funding the project "Molecularly controlled, stimuli-sensitive hydrogels for dynamically adjustable biohybrid actuators". S.S. and C.S. acknowledge funding of the Research Training Group RTG 2154 "Material for Brain" through the Deutsche Forschungsgemeinschaft. J.M. thanks S. Gutekunst for stimulating discussions. The authors thank L. Thormählen for magnetic thin film deposition.

**References:**

[1] S. Rampini, P. Li, and G. U. Lee, Lab Chip 16, 3645-3663 (2016). [2] U. Sajjad, E. Lage, and J. McCord, Adv. Mat. Int. 5, 1801201 (2018). [3] B. Lim, P. Vavassori, R. Sooryakumar, et al., J. Phys. D: Appl. Phys. 50, (2016). [4] T. Henighan, A. Chen, G. Vieira, et al., Biophys. Jour. 98, 412-417 (2010). [5] J. Pivetal, D. Royet, G. Ciuta, et al., J. Magn. Magn. Mat. 380, 72-77 (2015). [6] U. Sajjad, R. B. Holländer, F. Klingbeil, et al., J. Phys. D: Appl. Phys. 50, (2017). [7] F. Klingbeil, F. Block, U. Sajjad, et al., Sci. Rep. 10, 1-12 (2020). [8] A. Vansteenkiste, J. Leliaert, M. Dvornik, et al., AIP Adv. 4, 107133 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/515b7a81ae7380b50d0574aff749114e.jpg)
Fig. 1: Simulation data of a single MB motion for clockwise magnetic field rotation. Snapshots of the unidirectional motion together with the corresponding potential landscape are shown for four magnetic field angles. The corresponding matching experimental behavior for the same parameters are shown. The calculations and experiments were performed at clockwise rotating magnetic fields of 40 mT with a rotation frequency of 1.0 Hz.

![](https://assets.underline.io/uploads/markdown_image/1/image/c9bccb77854ad0f52c7d5fc0767f13c4.jpg)
Fig. 2: Forward transport of a microbead engulfed by a rat embryonic fibroblast cell. The initial position of the cell and the microbead on the upper side of an oval structure is marked, demonstrating a forward motion even under the condition of a starting velocity in the backward direction. Here a counterclockwise rotating magnetic field of 40 mT with a rotation frequency of 0.3 Hz is applied.

technical paper

Coupling piezoelectric and magnetoelastic materials together enables the electrical control of magnetism. However, the lack of an accurate non-linear magnetoelastic constitutive model complicates designing macroscale devices with these multiferroic composites. While micromagnetic simulations are the gold standard for mesoscale magnetic modeling, their use is limited to very small systems (i.e., typically below 10s of cubic microns). The focus of this research is on generating an accurate constitutive model for macroscale magnetoelastic materials that is consistent with micromagnetics. Multiple different constitutive models are currently used to describe macroscale magnetoelastic materials [1,2,3]. Two common approaches, polynomial and statistical energy models, each have their own strengths and limitations. For example, series expansion models that use polynomial expansions are straightforward to setup, however they are not capable of capturing the saturating behavior of magnetic materials. Additionally, to obtain nonlinear material properties well-controlled experiments to curve fit the models are required [4], which can be prohibitively challenging, time consuming, and expensive for anisotropic materials. Alternatively, statistical models can overcome the inherent limitations of polynomial expansions. These models utilize Boltzmann statistics to calculate the average magnetization and magnetostriction. These calculations account for the Zeeman, magnetoelastic, and magnetocrystalline anisotropy energies. A challenge of this statistical approach is that the requisite integral expressions do not possess general closed form solutions and therefore require numerical solutions. The first of these integrals is the partition function, which is dependent on the micromagnetic energies of the system u, and the thermal energy. In the title of Figure 1 the partition function includes beta which is used as a nondimensional term representing the magnitude of the micromagnetic energies in u. The other integral to consider is the average magnetization, which is derived from the partition function. While standard numerical integration methods can be utilized, they are computationally expensive, limiting their use in finite element models. In this work a constitutive model utilizing statistical physics to bridge micromagnetics to the macroscale is developed, and the accuracy and computational complexity of several integration methods are analyzed to produce a model suitable for use in high fidelity numerical models. The two methods for approximating the partition function that were examined are a partial series expansion and Laplace’s method. Conceptually a series expansion is asymptotically exact at the point its expanded about, conversely Laplace’s method is asymptotically exact at higher energy values (i.e., the methods are complimentary). The accuracy of each method was compared to an accurate, but computationally expensive numerical integral with relative error set at machine precision. The average magnetization, and therefore the partition function, has a closed form solution when only the Zeeman energy is included. If the additional micromagnetic energies are small compared to the Zeeman energy, they can be expanded in a Maclaurin series, which maintains integrals with exact solutions. Figure 1(a) shows the absolute error of this partial series expansion method as the magnitude of the applied energies (beta) increase. The inset graph also plots the absolute error, but beta 1 represents when only Zeeman energy is applied, and beta 2 shows when only the other micromagnetic energies are applied. Figure 1(b) shows the absolute error of Laplace’s method as the magnitude of the applied energies increase. The inset graph again considers the main contributor to the energy of the system. These two figures show that the two methods are indeed complimentary and so a hybrid model would maintain low relative errors for the entire range of beta values. Additionally, Laplace’s method only requires a small number of points (e.g., between two and six) to approximate integrals, making it more computationally efficient compared to standard integration methods. To conclude, we will use this model to simulate both the magnetization and magnetostriction of Galfenol subjected to magnetic fields up to 20 mT and mechanical stresses between -50 and 50 MPa. The results will be compared to experimental data from the literature [5].

**References:**

[1] P. G. Evans and M. J. Dapino, Journal of Applied Physics., Vol. 107, (2010) [2] Yining Li et al. Journal of Magnetism and Magnetic Materials., Vol. 472, p. 59–65 (2019) [3] Z. Xiao et al. ACS Applied Materials & Interfaces., Vol 12.5, p. 6752–6760 (2020) [4] Z. Xiao and S. Le, Journal of Applied Physics., Vol 100.6, (2006) [5] A. Mahadevan, P.G. Evans, and M.J. Dapino, Applied Physics Letters., Vol. 96, (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2ace4b46782f3a53b9f2bb7ecae3629c.jpg)
Figure 1: Absolute error of both approximation methods. (a) Results for partial series expansion (b) Results for Laplace's method

 Approximation Methods for Hybrid Constitutive Model of Magnetostriction

Large magnetostriction and magnetoelastic coupling are properties extensively sought after because of their exploitability in low power consumption devices, energy conversion, and spintronics. Many alloys displaying large magnetostriction coefficients contain rare earths, whereas Fe-Ga systems, being rare earths free, have attracted attention because of their significant magnetostrictive response, coupled with good corrosion resistance and mechanical hardness [1]. Magnetostriction is particularly significant in Fe-rich alloys, with Ga content approximately equal to 19% and 27%. However, in this range of compositions, the Fe-Ga binary system is characterised by the possible presence of multiple phases, whose complex interplay strongly affects the magnetostrictive response. The stabilisation of the A2 phase by means of suitable thermal treatments turns out to be an effective way to obtain remarkable magnetostrictive properties. In this work, Fe-Ga alloys, containing 18, 21 and 23 at.% of Ga, were prepared in bulk form by arc melting. In their as-cast state they display a small magnetostriction, that is strongly improved after annealing at 1000 °C for 24 h, and subsequent rapid cooling. Multiple characterisation techniques, such as X-ray diffraction, Differential scanning calorimetry, Mössbauer spectroscopy, temperature-dependent magnetisation curves, hysteresis loops, magnetic force microscopy and magnetostriction measurements were exploited in synergy to gain a deep understanding of the structure-properties relationships in the studied alloys, before and after annealing. The A2 phase, which is favoured in the lower range of compositions and is promoted at the expense of the D03 one by the annealing, is responsible for characteristic dendritic and maze magnetic domains, shown in Figure 1, reporting domains patterns acquired with a magnetic force microscope on as-cast and annealed samples of the three compositions. Conversely, the lower-contrast regions, especially in the Ga23 as-cast sample, are due to the D03 phase. The transformation of the D03 phase into the A2 one with annealing, followed through extensive microstructure investigations, is responsible for the strong improvement of the magnetostriction, which almost reaches 240 ppm (transverse configuration) in the alloys with 18 at.% of Ga, after annealing (Figure 2).

**References:**

[1] J. Atulasimha, A.B. Flatau, Smart Mater. Sctruct., Vol. 20, p.043001 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fb554383092a2de573f3c9c9372c7fef.jpg)
Fig. 1. MFM images of as-cast and annealed Fe-Ga bulk alloys with 18, 21 and 23 at.% of Ga. In the insets, FFT transforms of the same images.

![](https://assets.underline.io/uploads/markdown_image/1/image/f5d001f23cb724c503cddb52ce8186e5.jpg)
Fig. 2. Transverse magnetostriction as a function of Ga at.% for as-cast (blue curve) and annealed (red curve) samples.

 Phase Transformation and Magnetostriction in Fe100-xGax bulk alloys

Magnetoelastic sensors are typically amorphous ferromagnetic ribbons in which mechanical and magnetic properties are coupled, so an acoustic wave can be excited in these materials by the application of an alternating magnetic field and detected by the magnetic changes induced in it. The magnetoelastic ribbon can enter in resonance at certain frequencies of excitation, compatible with the dimensions and elastic properties of the material. These resonance frequencies are sensitive to different external parameters, which can be used to design different types of sensors [1], in particular, differences in ribbon mass loading cause a shift of the resonance frequency of the sensor. This sensitivity and its ability to query and detect remotely, made these devices especially interesting for sensing biological and chemical agents. In the present work, we have used magnetoelastic sensors to monitor the precipitation reaction of calcium oxalate crystals (CaC2O4), one of the most common minerals which form calcifications in the urinary track. The formation of these crystals was measured in real-time by tracking the changes in the resonant frequency of the sensor, which decreases as the precipitate is deposited on its surface (Figure 1), changing its total mass [2]. Previous works by Bouropoulos et al. have used magnetoelastic sensors based on the commercial material Metglas® 2826 for monitoring the kinetics of different precipitation reactions [3]; in this work a different amorphous ferromagnetic alloy ((Fe-Cr)-Based metallic glass of composition Fe73Cr5Si10B12) that has shown to have an improved corrosion resistance has been used [4]. This composition contains a small amount of chromium that allows the formation of a passivation layer on the material, thus favoring its corrosion-resistant behavior, which allows it to be used in biomimetic environments without any pre-treatment of its surface and avoid possible changes in the resonance frequency due to the corrosion of the ribbon. The precipitation reaction of calcium oxalate was carried out by mixing equal parts of solutions at the same concentration of oxalic acid and calcium chloride, and the formation of the insoluble salt crystals was monitored in a 500 s time interval. Solutions of different concentration (1, 5, 10, 30, 50 and 100 mM) were used in order to observe its effect on the rate of reaction (Figure 1). In addition, the monitoring of the reaction was complemented with the numerical fittings of the obtained resonance curves (Figure 2) to an analytical expression that describes the behavior of the resonance [5]. These numerical fittings improve the observation of the temporal evolution of the different parameters that characterize the response of the sensor (such as the resonance frequency, the damping parameters or the quality factor Q), and can be used to monitor the precipitation reaction, since in addition to a decrease in the resonance frequency, the deposition of calcium oxalate crystals on the ribbon causes an increase in the damping experienced by the sensor and therefore, a decrease in its quality factor. The numerical fittings made allowed to obtain this quality factor of the sensor with more accuracy than with traditional methods, which are unreliable when working with damped signals, such as when the sensor is immersed in a liquid and subject to mass loads. In addition, these fittings allow to get rid of the noise associated with the experimental measurements, which facilitates the calibration and use of the sensor. These fittings allow to follow the evolution of the precipitation reaction of calcium oxalate in a more reliable, precise and noiseless way.

**References:**

[1] C. Grimes, C. S. Mungle and K. Zeng, Sensors, Vol. 2, no 7, p. 294-313 (2002). [2] B. Sisniega, A. Sagasti, J. Gutiérrez and A. García-Arribas, Sensors, Vol. 20, no 10, p. 2802 (2020). [3] N. Bouropoulos, D. Kouzoudis and C. Grimes, Sensors and Actuators B: Chemical, Vol. 109, no 2, p. 227-232 (2005). [4] A. Sagasti, V. Palomares, J. M. Porro, Materials, vol. 13, no 1, p. 57 (2020). [5] B. Sisniega, J. Gutiérrez, V. Muto and A. García-Arribas, Materials, vol. 13, no 21, p. 4708 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bb7d61ffc90c7103cae1159d7944bdd0.jpg)
Fig. 1: Temporal evolution of the resonance frequency of the magnetoelastic sensor as the precipitation reaction progresses, for different concentration of reactants in the reaction (30, 50 and 100 mM) and a control measurement (sensor in a vial with distilled water).

![](https://assets.underline.io/uploads/markdown_image/1/image/924bd6ccec73727c2a3c30779f0becc9.jpg)
Fig. 2: Temporal evolution of the resonance curves of the magnetoelastic sensor during the precipitation reaction of calcium oxalate for the case of 30 mM concentration of reagents. As the reaction progresses, the resonant frequency and the quality factor Q of the curves decrease.

 Real Time Monitoring of the Precipitation of Calcium Oxalate by Using Corrosion Resistant Magnetoelastic Resonance Sensors

Magnetostrictive materials are distinguished by an inherent coupling between their mechanical and magnetic processes which is manifested as a direct (actuator) and an inverse (sensor) effect. Iron-gallium alloys (Galfenol, Fe100-xGax with 12&lt;x&lt;30) are a particularly promising magnetostrictive, transducer material that combines highly desirable tensile and compressive mechanical attributes with superior magnetic properties. These characteristics make it possible to design robust structural sensors and energy harvesters. However, the behavior of the mechanical and magnetic phenomena is essentially non-linear, making it difficult to develop analytical models to find an optimal operational condition. Because the magnetostriction strongly depends on both the pre-stress and magnetic field, the characterization of the material is usually conducted under controlled conditions for normalizing the parameters with respect to each other. In this study, large-grained, highly textured, polycrystalline Galfenol samples with 15, 17, 18, and 19 at. % Ga were evaluated. As shown in Figure 1(a), standard magnetic hysteresis loops were measured at various applied compressive stresses. Changes in the flux density, B, as a function of applied stress were determined as the intercept values at specific applied magnetic fields, shown by the red dotted line for the 50 Oe bias magnetic field condition. Figure 1(b) shows an example of the flux density as a function of the mechanical pre-stress at constant magnetic fields of 30, 50, 80, 100, 120, and 150 Oe for 18% Galfenol sample (colored dot symbols). To estimate the response of the magnetic flux density as a function of applied stress, a hyperbolic tangent function was used with 4-nonlinear parameters (a, b, c and d) which are functions of magnetic field, as defined below: B(T,H)=a(H)×tanh[b(H)×(T+c(H))]+d(H) (1) The calculated magnetization based on the fitted parameters is plotted in Figure 1 (b) with solid lines, which fits the experimental data well. The continuous magneto-mechanical sensitivity, defined as the slope of the magnetization versus stress data, was calculated from the fitted equation (1) and the magneto-mechanical sensitivity results are depicted in Figure 2 for various bias magnetic fields. The same data process procedure was applied for the experimental characterization data of 15, 17 and 19% Ga specimens and Figure 3 shows the maximum value of the magneto-mechanical sensitivity as a function of applied bias field for the various compositions of Galfenol. As can be seen in Figure 3, 17% Galfenol shows higher magneto-mechanical sensitivity than 18% Galfenol, which usually shows higher magnetostriction values. Based on the results in Figure 3, 17% Galfenol will give better performance for sensor and energy harvester applications as compared to 18% alloys, which are used for actuation.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ee2402680b3e12b17a954ad38c86b980.jpg)
Figure 1. (a) Flux-density (B) versus external applied magnetic field (H) at various pre-stress values (T). (b) Magnetic induction (B) versus external compressive stress (T) at various bias fields (H) and curve-fit results based on hyperbolic tangent function.

![](https://assets.underline.io/uploads/markdown_image/1/image/741346be7a511b6fbdbbcf08a654cc25.jpg)
Figure 2. (a) Magneto-mechanical sensitivity at various bias magnetic fields (30, 50, 80, 100, 120 and 150 Oe). (b) Magneto-mechanical sensitivity at various bias magnetic fields for various composition.

 A Calculation of Magneto-Mechanical Sensitivity for Various Compositions of Galfenol

Magnetic hyperthermia is one of the most promising biomedical applications of magnetic nanoparticles (NP) and is intended to be alternative to cancer therapies based on drug delivery and radiotherapy. It is based on the fact that magnetic NP dissipate heat when an oscillating magnetic field is applied to them in a quantity (specific absorption rate, SAR) that is closely related to the area of the hysteresis loop. The main problem in the field has become to find the suitable range of parameters that maximize SAR for a given material [1], SAR depends of course on the amplitude of the applied magnetic field and its frequency, but also on intrinsic parameters of the NP such as saturation magnetization, anisotropy, shape and size [2]. Although the role of external parameters is somehow well contrasted, there is still ongoing controversy on the role that dipolar interactions (DI) and aggregation state of the assemblies play on SAR. We will present results of Monte Carlo simulations of hysteresis loops of interacting NP assemblies in the macrospin approximation [3]. We will present first results of different regular spatial arrangements of NP, showing the influence of interparticle separation and particle size on SAR. Next, we will study the case of randomly placed NP with varying concentrations mimicking experimentally found situations [4] (inside and at the surface of liposomes/cells, clusters). It is found that formation of chain-like arrangements or assemblies with prolate shapes, lead to considerable increases in SAR due to DI. Acknowledgements: Work supported by Spanish MINECO (PGC2018-097789-B-I00), Catalan DURSI (2017SGR0598) and EU FEDER funds (Una manera de hacer Europa) also CSUC for supercomputer facilities.

**References:**

[1] S.-H. Noh, et al. Nano Today 13, 61 (2017); R. Hergt et al. Nanotechnology 21, 015706 (2010). [2] B. Mehdaoui, et al.Phys. Rev. B 87, 174419 (2013); R. P. Tan et al.Phys. Rev. B 90, 214421 (2014); P. Hasse and U. Nowak Phys. Rev. B 85, 045435 (2012); P. V. Melenev et al. Phys. Rev. B 86, 104423 (2012). [3] C. Martínez-Boubeta et al.Scientific Reports 3, 1652 (2013). [4] Brollo et al., Phys. Chem. Chem. Phys. 20, 17829 (2018); D. Niculaes et al., ACS Nano 11, 12121 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e6cf5b763ca228f2ac9da0bc2351d2af.jpg)
Concentration dependence of the hysteresis loop area for different kinds of NP random assemblies.

 Aggregates and Dipolar Interactions in Nanoparticle Assemblies for Magnetic Hyperthermia

Recent wearable ultrasensitive magnetometers opened novel applications of magnetoencephalography (MEG) to brain machine interface. In a recent study, the subject was allowed to move the head in a limited area of approximately 40 x 40 x 40 cm3 having a uniform magnetic field produced by a set of active shimming coils(1). The significant challenge of such wearable MEG systems is to improve the uniformity of magnetic field in the entire space in the magnetic shield room (MSR) and to suppress motion artifacts in MEG signals. A typical approach of realizing high field uniformity has been to make MSRs with highly symmetric shapes such as cylinder and polyhedron. However, these MSRs still require additional adaptive techniques to improve residual non-uniformity. The purpose of this study is to develop a new method of passive shimming for an MSR using ferromagnetic plates attached to its walls. The concept of this study is to optimize the spatial distribution of the magnetic field inside MSR with combination of ferromagnetic plates attached to the surface of MSR. The method mainly consists of two steps. In the forward problem, firstly, we calculated the spatial distributions of magnetic fields with the ferromagnetic plates of 601 mm (1 mm thickness) attached at 16 locations on the surface of a downsized magnetic shield box (MSB) of 200350 mm (1 mm thickness) (Fig. 1(a)). The uniformity was evaluated by obtaining the standard deviation for 9 measurement points inside the MSB. We established the relationship between the individual shimming plates and the resulting magnetic field uniformity inside MSR. Secondly, by solving the inverse problem based on the forward solution, we identified the optimum number of plates to be attached at each location. We used the Tikhonov regularization2) to solve the ill-posed inverse problem, and the L-curve method3) to determine its optimal parameters. In the experiments, we measured and evaluated the spatial distribution of magnetic fields using nine magneto-impedance (MI) sensors (ROHM BM1422AGMV), as shown in Figs. 1(b) and (c). We found one shimming steel plate caused magnetic field variation of 50 ~ 300 nTinside MSB in the forward problem. And then we let the value of magnetic field of 9 measurement points equal to zero and solve the inverse problem to find the number of shimming plates. Figure 2(a) shows the combination of the shimming plates optimized by the inverse problem. Figures 2(b) and (c) show the magnetic field distribution in the area of 120 x 120 mm inside MSB with and without the combination of shimming plates, respectively. The shielding factor increased 131% of MSB, from ~5 to ~8, by the proposed method. We also evaluated magnetic field uniformity by calculating the standard deviation of 9 measurement points inside MSB. The standard deviation is 0.211 and 0.379 with and without the shimming method, indicating the magnetic field uniformity inside MSB has improved 44% by the shimming method. Figures 2(d) and(e) show the magnetic field distribution measured by nine MI sensors in the area of 160 x 160 mm without MSB and with MSB, respectively. The experimental shielding factor is ~7, which is comparable to the simulation results. In conclusion, the proposed methods of passive shimming for an MSR using ferromagnetic plates demonstrates the feasibility of improving the magnetic field uniformity and is applicable to wearable MEG system in the future. This work was supported by MEXT Q-LEAP with the Grant Number JPMXS0118067395.

**References:**

(1) H. Niall, et al., NeuroImage 181: 760-774 (2018). (2) D. Calvetti, et al., Journal of Computational and Applied Mathematics 123.1-2: 423-446 (2000). (3) H. Christian, et al., "The L-curve and its use in the numerical treatment of inverse problems." (1999): 119-142.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/225e9eac620c2f7bd03e9d474e4e2734.jpg)
(a) Schematic of 16 shimming location and 9 measurement points of shimming design (b) Magnetic shield box assembled by steel. (c) Image of MI sensors setup. We used 9 MI sensors fixed on a resin board to measure the magnetic field distribution, distance of each sensor is 80 cm.

![](https://assets.underline.io/uploads/markdown_image/1/image/0a66a80a354d85830facd3503e6cfc5b.jpg)
Figure.2 (a) Number of plates on each shimming location. 2D Simulation results of (b) no shimming case and (c) with shimming case solved by inverse problem, Experiment results of (d) magnetic field distribution without MSB (Magnetic Shield Box) and (e) magnetic field distribution with MSB (Magnetic Shield Box)

 Shimming Design of Magnetic Shield Room Using Ferromagnetic Plates

Magnetic nanoparticles are an important asset in many biomedical applications ranging from the local heating of tumours[1] to targeted drug delivery towards diseased sites[2]. Recently, magnetic nanoflowers showed a remarkable heating performance[3,4] in hyperthermia experiments thanks to their complex structure leading to a broad range of magnetic dynamics. To grasp their full potential and to better understand the origin of this unexpected heating performance, we propose the use of Kaczmarz’ algorithm[5] in interpreting magnetic characterisation measurements[6]. It has the advantage that no a priori assumptions need to be made on the particle size distribution, contrasting current magnetic interpretation methods that often assume a lognormal size distribution. Both approaches are compared on DC magnetometry, magnetorelaxometry and AC susceptibility characterisation measurements of the nanoflowers. We report that the lognormal distribution parameters vary significantly between data sets, whereas Kaczmarz’ approach achieves a consistent and accurate characterisation for all measurement sets. Additionally, we introduce a methodology to use Kaczmarz’ approach on distinct measurement data sets simultaneously. It has the advantage that the strengths of the individual characterisation techniques are combined and their weaknesses reduced, further improving characterisation accuracy. Our findings are important for biomedical applications as Kaczmarz’ algorithm allows to pinpoint multiple, smaller peaks in the nanostructure’s size distribution compared to the monomodal lognormal distribution. The smaller peaks permit to fine-tune biomedical applications with respect to these peaks to e.g. boost heating or to reduce blurring effects in images. Furthermore, the Kaczmarz algorithm allows for a standardised data analysis for a broad range of magnetic nanoparticle samples. Thus, our approach can improve the safety and efficiency of biomedical applications of magnetic nanoparticles, paving the way towards their clinical use.

**References:**

 [1] A. Espinosa, R. Di Corato, J. Kolosnjaj-Tabi, et al, ACS Nano, Vol. 10, p. 2436–2446 (2016) [2] K. T. Al-Jamal, J. Bai, J. T.-W. Wang, et al, Nano Letters, Vol. 16, p. 5652–5660 (2016) [3] P. Bender, J. Fock, C. Frandsen, et al, J. Phys. Chem. C, Vol.122, p. 3068–3077 (2018) [4] C. Blanco-Andujar, D. Ortega, P. Southern, et al, Nanoscale, Vol. 7, p. 1768–1775 (2015) [5] S. Kaczmarz, Bulletin International de l’Academie Polonaise des Sciences et des Lettres, Vol. 35, p. 355–357 (1937) [6] J. Leliaert, D. Schmidt, O. Posth, et al, Journal of Physics D: Applied Physics, Vol. 50, p.195002 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d71e9f523e4a62d6a20fc7c82d90f1d3.jpg)
Best combined fit to a) the magnetorelaxometry measurement data and b) imaginary part of the AC-susceptibility measurement data of suspended nanoflowers using a lognormal distribution and using Kaczmarz’ method. c) The obtained relaxation time distributions corresponding to the fits in panel a) and b).

 Advanced analysis of magnetic nanoflower measurements to leverage their use in biomedicine

Additive manufacturing of smart materials is a novel field in engineering. The ability to produce adaptable materials in varying geometries opens the door to the creation of a tremendous variety of new sensors, actuators and applications in domains including, transportation, energy production and medicine [1][2]. In this work, our objective is to build a ferromagnetic catheter by using additive manufacturing principles employed for the creation of smart materials (Fig. 1). Induction heating phenomena takes place in the ferromagnetic catheter due to the influence of a varying magnetic excitation field. This contactless heat source can be used to heal locally and destroy damaged blood vessels. According to medical specialists, thermal ablation of varicose veins requires a temperature close to 120°C and time constants lower than a few seconds [3]. First investigation results showed great potential for success using the low frequency induction heating (LFIH) method but further surveys and validation steps are still needed before in vivo testing can commence. Fig. 1 – Illustration of the ferromagnetic catheter. In this study, multi-physics simulation results, including ferromagnetic, thermal and fluid mechanics domains were compared to experimental data, then conclusions are proposed to establish the most adapted magnetic waveform (frequency) and its influence on the human tissues. In our processs, heat is transferred through a contactless method. The flexible 3D printed ferromagnetic catheter is subjected to an alternating magnetic excitation. Under the influence of the magnetic excitation, eddy currents are generated through the catheter creating heat. First published results [4][5] describing this technique have experimentally demonstrated the feasibility of heat generation but the conditions tested and simulated were still far from the in vivo environment. In this study, we go deeper into the investigation process, we propose simulation results (magnetic, thermal …) under much realistic experimental conditions. In [4], the authors limit the magnetic excitation signal to a few kHz. The purpose is to avoid undesired charge displacements in the surrounding tissue, but this restriction is strictly assumption based and further investigations must be under-taken to determine the optimal value for ablation while minimizing charge displacement. No further investigations have been proposed to establish a significant cutoff frequency. In this new research, a ferromagnetic model for the simulation of the ferromagnetic composite magnetic behavior is developed first. This model is based on previous work on the same topic [6]-[8] and it investigates the frequency dependence of the composite hysteresis area, i.e. the heat generated through the LFIH influence. Next, comparisons between the model and experimental situations are investigated to set the ferromagnetic model parameters and to establish the most efficient LFIH frequency. Finally, multi-physics simulation results combined with experimental tests are reviewed to predict the ferromagnetic composite’s behavior on living tissues under the influence of the optimized magnetic excitation. Before validating the ferromagnetic catheter as a realistic treatment method for varicose veins, special attention must be given to the undesired charges or ionic displacements in the healthy surrounding tissues causing local temperature elevations and degradations. A compromise between treatment and negative effects on surrounding tissue must be made to establish the best working frequency. Numerical simulations are proposed to establish the optimized configuration of the magnetic source (frequency, amplitude) and of the ferromagnetic catheter behavior, these results constitute a huge step toward a first medical test.

**References:**

[1] Standard A. F2792, Pa, USA: ASTM International (2012) [2] G.N. Levy & al., CIRP Annals-Manuf. Technol., vol. 52 iss.2, pp. 589-609 (2003) [3] S. Nehemiah & al., Cochrane Library, iss. 13 (2013) [4] Z. Xiang & al., polymers 2020, 12(2), 386 (2020) [5] Z. Xiang & al., Mat. & Des., Vol. 174, 107804 (2019) [6] M. A. Raulet & al., IEEE Transactions on Magnetics, vol. 40, n° 2, pp. 872 – 875 (2004) [7] Z. Xiang & al., IEEE Trans. on. Mag, IEEE int. Mag. Conf. (INTERMAG), Singapore (2018) [8] B. Gupta & al., Proc. of the 21st int. conf. on the comp. of electromag. fields COMPUMAG, Daejeon (S. Korea), (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7cd27e86849e75379de11a4ef8f53341.jpg)

 Low frequency Induction heating of a ferromagnetic catheter for the varicose veins treatment: study of feasibility

Mn-doped ferrite nanoparticles are promising materials for applications in biomedicine as they exhibit better properties for some biomedical applications than non-doped magnetite or maghemite. [1] The thermal decomposition of metal precursors in an organic solvent is arguably the best method in terms of size control and the magnetic properties of the so-obtained materials. It provides hydrophobic nanoparticles that must be transferred to water through surface modification procedures before their use in biomedicine. In this work, Mn-doped ferrite nanoparticles have been synthesized by thermal decomposition changing systematically the Mn/Fe ratio of the metal precursors. Then, they have been transferred to the aqueous phase through ligand substitution with dimercaptosuccinic acid and dopamine. We show that the synthesis and post-synthesis manipulations lead to changes in the composition. During the thermal decomposition process, Mn is incorporated in the nanoparticles in a relatively lower amount than Fe and, then, during the surface modification step both Mn and Fe ions leach out from the nanoparticles (Figure 1). This alteration of the chemical identity of the nanoparticles have substantial implications for their subsequent application because small variations in the Mn/Fe ratio have a strong impact on properties like the saturation magnetization, blocking temperature, contrast enhancement for magnetic resonance imaging, magnetic heating, as well as on the cytotoxicity.[2]

**References:**

[1] L. Yang et al., Chem. Mater., Vol. 29, p.3038 (2017). [2] D. García-Soriano et al., J. Colloid Interf. Sci., Vol. 578, p.510 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a4b3867c47619b2ddabcdcd15281883f.jpg)
Scheme illustrating the changes in composition when the nanoparticles are transferred from an organic dispersion to an aqueous one.

 Cation leaching alters the properties of Mn nanoferrites for biomedical applications

The advances in synthesis methods and the research of new magnetic effects have been the driving forces propelling the use of magnetic nanostructures in several research fields. In biomedical applications, magnetic nanoparticles, usually in the superparamagnetic state, are mainly used in magnetic fluid hyperthermia (MFH) and as contrast agents. In contrast, the novel magnetic nanostructures (MNS) studied in this work present a unique spin arrangement in the magnetic ground state, namely spin-vortex or synthetic antiferromagnetic state. MNS are mainly produced using top-down lithography techniques and physical vapour deposition methods. They are not spherical, rather disc-shaped, like coins with nanometer dimensions. MNS showed promising results in cell separation, as a contrast enhancing agents in MRI and in magneto-mechanically induced cell annihilation. Magneto-mechanically induced cell annihilation is a comparable technique with MFH for cancer therapy, where instead of superparamagnetic particles, micro/nano-discs in the spin-vortex state or synthetic antiferromagnetic nanostructures are employed. The main advantages of this novel approach are the usage of weaker magnetic fields with lower frequencies, as well as the need for a lower concentration of particles. This scenario opens new possibilities in cancer therapy, having triggered a scientific interest for MNS with unique spin configurations suitable for biomedical applications [1]. In this work, we developed one subset of biocompatible magnetic nanostructures that exhibit a spin-vortex state with interest in analysing their application in magneto-mechanically induced cell death [2]. First, micromagnetic simulations, using mumax3 of sub-micron iron discs, were performed for different interdot distance and aspect-ratio (thickness/diameter), to better understand the magnetic behaviour of these nanostructures. Two sets of samples were studied: ideal circular discs and disc-shaped nanostructures (based on images of real samples). By analysing the nucleation and annihilation fields, as well as the magnetic susceptibility, it was found that the (ideal) discs could be considered as isolated for interdot distances greater than twice the radius of the disc (2R) [3]. We also found that discs with an aspect ratio between 5 and 15 should sustain the vortex state in remanence. Iron nano-discs, with a diameter of about 500 nm, were fabricated by electron beam evaporation on a Si substrate pre-patterned by interference lithography [4]. The discs, protected by bottom and top gold layers, were fully characterized with scanning electron microscopy (SEM), X-ray diffraction (XRD), superconducting quantum interference device (SQUID), magneto-optic Kerr effect (MOKE) and ferromagnetic resonance (FMR) techniques. The synthesized nanostructures showed the desired vortex state configuration. The obtained magnetic measurements are in good agreement with the micromagnetic simulations (Fig. 1). Then, the magnetic vortex nano-discs were released from the substrate by chemical etching of a sacrificial layer. Subsequently, cell viability and uptake assays were performed in a human leukaemia monocyte cell line (THP-1). Several concentrations of nano-discs were studied by flow cytometry. As a result, the discs were internalized by the cells and found to be innocuous to them, in the absence of an external magnetic field. Work supported by Horizon 2020 MSCA grant agreement No 734801, AEI PID2019-104604RB, IT1162-19, IF/01159/2015, SFRH/BD/148563/2019, POCI-01-0145-FEDER-028676/PTDC/CTM-CTM/28676/2017 and POCI-01-0145-FEDER-031302/PTDC/FIS-MAC/31302/2017.

**References:**

[1] L. Peixoto, R. Magalhães, D. Navas, S. Moraes, C. Redondo, R. Morales, J. P. Araújo, C.T. Sousa, Magnetic nanostructures for emerging biomedical applications. Appl. Phys. Rev., 7 (2020) 011310., [2] Y. Cheng, M. E. Muroski, D.C.M.C. Petit, R. Mansell, T. Vemulkar, R. A. Morshed, Y. Hana, I. V. Balyasnikova, C.M. Horbinski, X.Huang, L. Zhangc, R. P. Cowburn, M. S. Lesniak, J. Control. Release 223 (2016) 75. [3] L. Peixoto, C. Sousa, D. Navas, and J. P. Araújo, Micromagnetic study of the vortex state in sub-micron iron discs. EPJ Web of Conferences 233 (2020) 05002. [4] B. Mora, A. Perez-Valle, C. Redondo, M.D. Boyano, R. Morales, ACS Appl. Mater. Interfaces 10 (2018) 8165.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/68db60cda0b5971db06d25b5e8aea1a8.jpg)

Unidirectional Transport of Superparamagnetic Beads and Biological Cells along an Oval Shaped Magnetic Element Path

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Unidirectional Transport of Superparamagnetic Beads and Biological Cells along an Oval Shaped Magnetic Element Path

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