France



There has been a recent interest in the use of magnetoelastic materials to develop new magnetic antenna technologies [1,2,3]. Magnetic antennas show promise for surpassing shortcomings in current technologies, such as communicating in lossy environments (e.g., underground or underwater). One commonly proposed design is a resonant composite multiferroic beam consisting of magnetoelastic, elastic, and piezoelectric layers. Appling a voltage to the piezoelectric layer causes the beam to bend, straining the magnetoelastic layer, modulating the magnetic field around the antenna, thereby transmitting information. Current analytical and finite element magnetoelastic beam models [4,5,6] appear to work well for sufficiently long and thin structures, however the analytical models often neglect or overly simplify the magnetostatic field (i.e. demag) or spatially distributed material properties such as Young’s modulus or piezomagnetic coupling coefficients. Therefore, an analysis of under what conditions reduced-order analytical models are valid is needed before they can be used as a tool for analyzing general geometries where complex magnetic field distributions are expected. This work presents a detailed comparison of a finite element model and an analytical reduced order Euler-Bernoulli beam model with the goal of determining under what conditions the reduced order model is valid, and which foundational assumptions are responsible for any discrepancies.&lt;br/&gt;Both the finite element model and the analytical reduced order Euler-Bernoulli beam are set up to solve the same geometry, governing equations, and boundary conditions. The antenna has a simple geometry composed of three rectangular plates; with a linear elastic layer sandwiched between piezoelectric and magnetoelastic layers. The governing equations consist of the equations of magnetostatics, electrostatics, and linear elasticity (i.e., suitable for a near-field antenna operating at low kHz frequencies). The mechanical boundary conditions are setup to model a free-free Euler Bernoulli beam.&lt;br/&gt;The finite element analysis is conducted in a series of steps. First, a uniform magnetic field is applied, and the bias state of the antenna is solved for using a coupled, nonlinear, magnetoelastic constitutive model (along with linear elastic, and piezoelectric behaviors). A linearized modal analysis is then performed around this bias state to determine the dynamic eigenmodes of the mechanical vibrations. Once found, the first eigenmodes is subsequently used to model the mechanical deformation, which is then fed into the nonlinear magnetic material model to obtain the dynamic magnetization changes (i.e., a one-way coupled model, with mechanics driving the magnetics). The reduced order Euler-Bernoulli beam model is constructed using a similar approach. A bias strain distribution for a composite Euler-Bernoulli beam is first computed. In contrast to the FEA model, this assumes a spatially uniform demag factor, and spatially uniform material properties. A linearized eigenmode analysis is then performed that utilizes a linear piezomagnetic approximation to obtain a fully-coupled linearized solution.&lt;br/&gt;Both the finite element model and the analytical model have their strengths and weaknesses. The finite element model produces more accurate results utilizing spatially non-uniform and nonlinear material properties, and an accurate description of demag. However, the speed of the analytical model greatly outperforms the finite element model making it more suitable for understanding design alternatives and optimization. This work will examine how the assumption of uniform material properties and demag fields affects the accuracy of the analytical model and determine under what conditions the approximations are valid. Fig. 1 shows an example, from the finite element model, of the spatially distributed piezomagnetic coupling in the magnetoelastic material where the maximum coupling is found to be at the end of the beam. A specific focus will be made on examining the validity of using an analytical model to optimize the geometry of a magnetic antenna.

**References:**

J. Domann, and G. Carman.&lt;i&gt; Journal of Applied Physics&lt;/i&gt; Vol. 121(4), p.044905 (2017)&lt;br/&gt;J. Xu, C. Leung, X. Zhuang et al. &lt;i&gt;Sensors&lt;/i&gt; Vol.19(4), p.853 (2019)&lt;br/&gt;C. Dong, Y. He, M. Li et al. &lt;i&gt;IEEE Antennas and Wireless Propagation Letters&lt;/i&gt; Vol. 19(3), p.398–402 (2020)&lt;br/&gt;L. Shu, M. Dapino, P. Evans, et al. &lt;i&gt;Journal of Intelligent Material Systems and Structures&lt;/i&gt; Vol. 22(8), p.781–93 (2011)&lt;br/&gt;H. Zhou, and Y. Zhou. &lt;i&gt;Smart Materials and Structures&lt;/i&gt; Vol. 16(1), p.198–206 (2007)&lt;br/&gt;V. Guerrero, and R. Wetherhold. &lt;i&gt;Journal of Applied Physics&lt;/i&gt; Vol. 94(10), p.6659–66 (2003)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ca0752a517da73cb8517cd348fe69b9c.jpg)
Fig. 1.  Spatially distributed piezomagnetic coupling coefficient in the magnetoelastic layer of the beam.  Note that the image is from the finite element model where quarter symmetry is utilized (center of the beam is the bottom right corner).



INTERMAG 2021

 Validation of a Reduced Order Magnetoelastic Beam Model

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This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

There has been a recent interest in the use of magnetoelastic materials to develop new magnetic antenna technologies [1,2,3]. Magnetic antennas show promise for surpassing shortcomings in current technologies, such as communicating in lossy environments (e.g., underground or underwater). One commonly proposed design is a resonant composite multiferroic beam consisting of magnetoelastic, elastic, and piezoelectric layers. Appling a voltage to the piezoelectric layer causes the beam to bend, straining the magnetoelastic layer, modulating the magnetic field around the antenna, thereby transmitting information. Current analytical and finite element magnetoelastic beam models [4,5,6] appear to work well for sufficiently long and thin structures, however the analytical models often neglect or overly simplify the magnetostatic field (i.e. demag) or spatially distributed material properties such as Young’s modulus or piezomagnetic coupling coefficients. Therefore, an analysis of under what conditions reduced-order analytical models are valid is needed before they can be used as a tool for analyzing general geometries where complex magnetic field distributions are expected. This work presents a detailed comparison of a finite element model and an analytical reduced order Euler-Bernoulli beam model with the goal of determining under what conditions the reduced order model is valid, and which foundational assumptions are responsible for any discrepancies. Both the finite element model and the analytical reduced order Euler-Bernoulli beam are set up to solve the same geometry, governing equations, and boundary conditions. The antenna has a simple geometry composed of three rectangular plates; with a linear elastic layer sandwiched between piezoelectric and magnetoelastic layers. The governing equations consist of the equations of magnetostatics, electrostatics, and linear elasticity (i.e., suitable for a near-field antenna operating at low kHz frequencies). The mechanical boundary conditions are setup to model a free-free Euler Bernoulli beam. The finite element analysis is conducted in a series of steps. First, a uniform magnetic field is applied, and the bias state of the antenna is solved for using a coupled, nonlinear, magnetoelastic constitutive model (along with linear elastic, and piezoelectric behaviors). A linearized modal analysis is then performed around this bias state to determine the dynamic eigenmodes of the mechanical vibrations. Once found, the first eigenmodes is subsequently used to model the mechanical deformation, which is then fed into the nonlinear magnetic material model to obtain the dynamic magnetization changes (i.e., a one-way coupled model, with mechanics driving the magnetics). The reduced order Euler-Bernoulli beam model is constructed using a similar approach. A bias strain distribution for a composite Euler-Bernoulli beam is first computed. In contrast to the FEA model, this assumes a spatially uniform demag factor, and spatially uniform material properties. A linearized eigenmode analysis is then performed that utilizes a linear piezomagnetic approximation to obtain a fully-coupled linearized solution. Both the finite element model and the analytical model have their strengths and weaknesses. The finite element model produces more accurate results utilizing spatially non-uniform and nonlinear material properties, and an accurate description of demag. However, the speed of the analytical model greatly outperforms the finite element model making it more suitable for understanding design alternatives and optimization. This work will examine how the assumption of uniform material properties and demag fields affects the accuracy of the analytical model and determine under what conditions the approximations are valid. Fig. 1 shows an example, from the finite element model, of the spatially distributed piezomagnetic coupling in the magnetoelastic material where the maximum coupling is found to be at the end of the beam. A specific focus will be made on examining the validity of using an analytical model to optimize the geometry of a magnetic antenna.

**References:**

J. Domann, and G. Carman. Journal of Applied Physics Vol. 121(4), p.044905 (2017) J. Xu, C. Leung, X. Zhuang et al. Sensors Vol.19(4), p.853 (2019) C. Dong, Y. He, M. Li et al. IEEE Antennas and Wireless Propagation Letters Vol. 19(3), p.398–402 (2020) L. Shu, M. Dapino, P. Evans, et al. Journal of Intelligent Material Systems and Structures Vol. 22(8), p.781–93 (2011) H. Zhou, and Y. Zhou. Smart Materials and Structures Vol. 16(1), p.198–206 (2007) V. Guerrero, and R. Wetherhold. Journal of Applied Physics Vol. 94(10), p.6659–66 (2003)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ca0752a517da73cb8517cd348fe69b9c.jpg)
Fig. 1. Spatially distributed piezomagnetic coupling coefficient in the magnetoelastic layer of the beam. Note that the image is from the finite element model where quarter symmetry is utilized (center of the beam is the bottom right corner).

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Introduction: Magnetocaloric refrigeration is an emerging technology that shows significant potential to reduce the dependence on traditional vapor compression systems that support most of the cooling and refrigeration needs. Unlike significant body of work on the development of magnetocaloric materials, only a limited number of reports address their functional and chemical stability. This study focuses on a known refrigerant – intermetallic compound of lanthanum, iron, and silicon with minor amounts of cobalt, La(Fe0.84Co0.07Si0.08)13, and its stability in a standard heat exchange fluid, that is, water [1]–[3]. Experimental Details: An alloy with a nominal composition of La(Fe0.84Co0.07Si0.08)13 weighing 20 g was prepared by arc-melting of the elements under argon atmosphere on a water-cooled Cu-hearth. The ingot was re-melted four times, being turned over each time to achieve homogeneity. The total measured weight loss was less than 0.5 wt. %. The as-cast ingot was broken into smaller pieces, which were wrapped in a tantalum-foil, sealed inside a fused-silica tube under vacuum, and annealed at 1050°C for one week, followed by quenching in ice-cold water. Powders from the annealed pieces were prepared by crushing and grinding in an agate mortar with an agate pestle inside an argon-filled glove box and screened to particle sizes of 100 µm and below. Thus, prepared powder was divided into two samples. One sample was stored in deionized water and another in air, both for 14 days. Magnetic measurements were carried out using the Physical Property Measurement System (PPMS) VersaLab and PPMS Dynacool, whereas heat capacity was measured using PPMS Dynacool [4], [5]. Results and Discussions: Figure 1 presents ΔS vs. T calculated from magnetization isotherms and Fig. 2 shows the same calculated from heat capacity data after ground powders were stored in water and air. Both sets of data are in good agreement. The powders stored in water exhibit larger magnetocaloric effects by ~40% when compared to the same after stored in air. The most likely reason is nearly complete dissolution of the smallest particles in water, leaving behind only the largest particles with relatively low concentration of surface reaction products. Storing in air, on the other hand, likely leads to severe oxidation of the smallest particles but does not remove them from the material, thus effectively reducing the measured magnetocaloric effect. Further analysis of the powders to confirm this hypothesis is underway and the results will be reported in due time. Acknowledgment: Ames Laboratory is operated for the U.S. Department of Energy (DOE) by Iowa State University of Science and Technology under contract No. DE-AC02-07CH11358. Work at Ames Laboratory was supported by the U.S. DOE, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division.

**References:**

[1] F. Hu, B. Shen, J. Sun, Z. Cheng, G. Rao, and X. Zhang, “Influence of negative lattice expansion and metamagnetic transition on magnetic entropy change in the compound LaFe11.4Si1.6,” Appl. Phys. Lett., vol. 78, no. 23, pp. 3675–3677, Jun. 2001, doi: 10.1063/1.1375836. [2] F. X. Hu et al., “Magnetocaloric effect in itinerant electron metamagnetic systems La(Fe1−xCox)11.9Si1.1,” J. Appl. Phys., vol. 97, no. 10, p. 10M303, May 2005, doi: 10.1063/1.1847071. [3] L. Mañosa et al., “Inverse barocaloric effect in the giant magnetocaloric La-Fe-Si-Co compound.,” Nat. Commun., vol. 2, p. 595, Jan. 2011, doi: 10.1038/ncomms1606. [4] K. Javed, S. Gupta, V. K. Pecharsky, and R. L. Hadimani, “Stability of magnetocaloric La(FexCoy Si1-x-y )13 in water and air,” AIP Adv., vol. 9, no. 3, p. 035239, Mar. 2019, doi: 10.1063/1.5080108. [5] D. Clifford, V. Sharma, K. Deepak, R. V. Ramanujan, and R. Barua, “Multicaloric Effects in (MnNiSi)1-x (Fe2Ge)x Alloys,” IEEE Trans. Magn., pp. 1–1, 2020, doi: 10.1109/TMAG.2020.3025002.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c7b87e1a7d4cdbd8c05245787b4a63d1.jpg)
Fig.1: Comparison of ΔS vs T calculated using Maxwell's equation for samples stored in air and water for ΔH = 3T.

![](https://assets.underline.io/uploads/markdown_image/1/image/a6b1b75cb35af4ff1e22c0837bdc6f80.jpg)
Fig. 2 Comparison of ΔS vs T calculated using heat capacity measurements for samples stored in air and water for ΔH = 3 T.

 Chemical stability of magnetocaloric La(FexCoySi1-x-y)13 particles

Magnetocaloric effect (MCE) receives an increasing interest for its promising applicability in energy efficient refrigerators. Among the different magnetocaloric materials having potential applications for cooling devices that operate near room temperature, those exhibiting a first-order phase transition (FOPT) usually show larger responses than those exhibiting a second-order phase transition (SOPT), but the intrinsic hysteresis could be deleterious for cyclic operations [1]. Some FOPT materials such as Heusler alloys can also exhibit the Curie transition of their magnetic phases, thus leading to alloys exhibiting both direct (positive isothermal entropy change, ΔSiso) and inverse MCE (negative ΔSiso). However, the close proximity of the two types of transitions can produce a convoluted and compensated global response due to the different nature, direct and inverse, of their MCEs [2]. In order to evaluate the potential of the FOPT for magnetocaloric applications and, therefore, ascertain the usefulness of tuning the Curie temperature of the alloy by compositional modifications, it is necessary to be able to deconvolute its responses. It has previously been shown that concurrent SOPTs can be deconvoluted by applying the scaling laws of the MCE [3]. In this work, we propose an extension of the methodology to deconvolute concurrent FOPT and SOPT. For this purpose, a Heusler alloy with stoichiometry Ni48.1Mn36.5In15.4 has been used as a model case. Upon heating, this sample exhibits a FOPT from a low magnetization martensite to an austenite with higher magnetization. This magneto-structural transition produces an inverse MCE that is immediately followed by the Curie transition of the austenite, with its corresponding conventional MCE. With increasing the magnetic field, two different behaviors are observed: 1) the onset of the FOPT shifts to lower temperatures, with a peak ΔSiso value that increases abruptly at the beginning, reaches a maximum for ~5 T and subsequently decreases, and 2) a Curie transition whose response increases gradually in height and width, with a peak position that remains almost field independent. Due to the proximity of these two competing transitions, the overlapping of their responses increases with increasing field. The application of the scaling laws for the SOPT magnetocaloric response allows us to deconvolute the contributions of the two transitions. Top panel of Fig. 1 shows the experimental ΔSiso of the sample together with its reconstructed response. The separated contributions of the two phase transitions are presented in the bottom panel of Fig. 1. The good agreement between experimental and reconstructed curves allows us to reach the following conclusions: - Universal scaling can be used to deconvolute overlapping first and second order phase transitions. - The broadening of the SOPT with increasing field causes a larger overlap between transitions despite the shift of the FOPT to lower temperatures. - The experimental decrease of the inverse MCE peak above ~5T is due to the competing contribution of the SOPT and is not intrinsic to the FOPT. This deconvolution methodology allows to extract the information of the different phase transitions in the material without having to experimentally synthesize new alloys with different compositions. Work supported by AEI/FEDER-UE (grant PID2019-105720RB-I00), US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746), and Army Research Laboratory under Cooperative Agreement Number W911NF-19-2-0212.

**References:**

[1] V. Franco, J.S. Blázquez, J.J. Ipus, J.Y. Law, L.M. Moreno-Ramírez, A. Conde, Prog. Mater. Sci. 93 (2018) 112–232. [2] J. Y. Law, Á. Díaz-García, L. M. Moreno-Ramírez, V. Franco, A. Conde, A. K. Giri, Acta Mater. 166 (2019) 459. [3] Á. Díaz-García, J. Y. Law, P. Gebara, V. Franco, JOM 72 (2020) 2845–2852.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/181f71a01791952162fe6704a962d0ff.jpg)
Fig. 1 (Top panel) Experimental temperature dependence of ΔSiso of Ni48.1Mn36.5In15.4 Heusler alloy for different magnetic fields (open symbols) and its reconstructed ΔSiso response (stars symbols). (Bottom panel) Temperature dependence of ΔSiso for different fields of the deconvoluted responses of the SOPT (open symbols) and the FOPT (solid symbols).

 Deconvolution of First and Second Order Phase Transitions using the Scaling Laws of the Magnetocaloric Effect

Magnetocaloric materials with a first order phase transition exhibit thermal hysteresis, which is one of the key limiting factors that prevent their efficient implementation in magnetic refrigerators. This problem has to be tackled in a twofold way: a) understanding the different sources of thermal hysteresis of technologically relevant materials in order to minimize them, and b) predicting the response of the materials upon an arbitrary sequence of excitations, so that the trajectories of the minor loops in the M(T,H) space is known and their behavior in a magnetic refrigerator can be suitably modeled. To achieve those, in the recent years, the temperature variant of the first order reversal curves technique (T-FORC) has been proposed as a fingerprinting method for the characterization of thermal hysteresis in magnetocaloric materials [1]. This initial approach has been expanded in two complementary directions: the implementation of a faster characterization technique that makes use of an effective temperature approach (T*FORC) [2], and the development of models of the phase transformation that provide a physical meaning to the distinct features observed in experimental T-FORC distributions [3]. In this presentation we will show an overview of the T-FORC technique and highlight its potential for the characterization of hysteretic thermomagnetic phase transitions by applying it to two different Heusler alloys of the Ni50Mn34In16 family, with similar Curie temperatures but different temperatures of the martensitic transition (see figure). Experiments have been performed upon cooling and heating for different fixed values of magnetic field. The different relative distance between transitions leads to different features in their T-FORC distributions. The comparison of the experimental distributions with those obtained from the model of the magneto-structural transitions allows us to associate the distinct T-FORC features to different characteristics of the transformations. The existence of different rates during the transition is what mainly defines the features of the T-FORC distributions. The model also allows us to separate the effects of the structural transformation and the temperature dependence of magnetization of the martensitic and austenitic phases, making us conclude that T-FORC distributions mainly reveal the characteristics of the structural component of the hysteretic transition. The appearance of a negative elongation in the cooling mode T-FORC (and positive in the heating one) is associated to the significant temperature dependence of the magnetization of both pure phases. Work supported by AEI/FEDER-UE (grant PID2019-105720RB-I00), US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746), Army Research Laboratory under Cooperative Agreement Number W911NF-19-2-0212, Sevilla University under VI PPIT-US program, and by the FRIMAG project, funded by Emilia Romagna region within the 2014-20 POR-FESR program (CUP E32F16000190007). The authors thank Dr. Cecilia Bennati for her contributions on the synthesis of the samples.

**References:**

[1] V. Franco, T. Gottschall, K.P. Skokov, O. Gutfleisch, IEEE Magn. Lett. 7 (2016) 6602904. [2] L.M. Moreno-Ramírez, V. Franco, Metals 10 (2020) 1039. [3] V. Franco, J. Appl. Phys. 127 (2020) 133902.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6ed8091fdfb1e863af4f3a30dd0be729.png)
Magnetothermal hysteresis loops for (a) Ni49.65Mn34.19In16.17 and (c) Ni49.42Mn34.35In16.23 alloys with their corresponding T-FORC distributions, (b) and (d) respectively, where white dashed lines indicate schematically the most relevant features: (1) main peak distorted downwards; (2) elongation along the +45o direction that forms a ridge; (3) sinking to negative values.

 T-FORC as a tool for the characterization of magnetocaloric materials: from experiments to models

Since the discovery of the Giant Magnetocaloric Effect (MCE) on Gd5Si2Ge2 by Pecharsky and Gschneidner [1], the Gd5(Si1-xGex)4 family compounds have been intensively studied for applications in magnetic refrigeration (MR) at room temperature. The vast investigation at the macroscale on these alloys up to this time revealed many other important properties, such as giant magnetoresistance and colossal magnetostriction (CMS) [2]. Such behaviors arise from a strong magneto-volume coupling extreme sensitivity to variation of external (e.g., temperature, magnetic field, and pressure) and internal (e. g., stoichiometry, dimensionality, and doping) parameters. For this reason, this family compound presents a rich phase diagram that, for example, gives a wide range of temperatures for device operations. However, the low mechanical stability and oxidations issues are some drawbacks for long periods of appliance operation. Reducing it to the micro and nanoscales can improve the alloys' properties and also find novel properties. In the last years, some experimental approaches have been used to produce micro/nanostructures of Gd5(Si,Ge)4 [3]. It is possible to mention high-energy ball milling, RF magnetron sputtering, and laser ablation techniques, being the most promising. Using a femtosecond pulsed laser deposition, our group successfully obtained Gd5Si1.3Ge2.7 nanogranular film composed of 80 nm particles presenting a magnetostructural transition [4] and a negative thermal expansion [5]. Although this evidence revealed the great potential of ultrashort laser ablation, a more conventional and low-cost technique should be pursued aiming practical applications of these compounds. For example, Tarasenka et al. were able to produce colloidal suspensions of Gd-Si-Ge nanoparticles in liquid with a more accessible Nd:YaG nanosecond pulsed laser [6]. Although the NPs presented fine crystalline features, the formation of silicon carbide and particle segregation after an additional laser ablation occurs. Given this, in addition to finding the most appropriate experimental technique, reasonable control of the intrinsic structures is essential to optimize the material production on a large scale. Here, we demonstrate that a more simple gas-phase synthesis using a Nd:YaG and KrF Excimer nanosecond pulsed lasers can be used to produce Gd5(Si1-xGex)4 nanostructures with x = 0, 0.45 and 0.60. The stoichiometries were selected to cover all the possible structures adopted by this family: orthorhombic-II [O(II)] for x = 0; monoclinic (M) of x = 0.45; and orthorhombic-I [O(I)] for x = 0.60. It is worth mentioning that x = 0.45 and 0.60 are in the vicinity of the phase-mixed region to show the feasibility of this method along with the family phase-diagram. In particular, the KrF Excimer was chosen due to the laser wavelength that presents higher penetration depth and reduced reflectance in metals. The nanostructures were obtained by ablating the polished surface of ingots produced by tri-arc melting with 10 Hz of frequency and maximum energy of 550 mJ and 200 mJ, for Nd:YaG and KrF Excimer lasers, respectively. The chamber was pumped several times down to a base pressure of 10-6 Torr to prevent oxidation. During the deposition, Argon inert gas was used in a continuous flux in constant pressure of 1 Torr inside the chamber. From this process, Gd5(Si,Ge)4 grains with an average particle size between 10-30 nm were achieved with good crystalline features, as can be seen in Fig.1(a). Synchrotron X-ray Diffraction confirmed the great level of the structures crystallinity and revealed a change in symmetry for x = 0 and 0.45 respectively from O(II) and M to O(I). The structural shrinkage was found to be around 2% for the Si-rich compositions and less than 1% for Gd5Ge4 (x=0). Given the lower unit cell volume for the O(I) structure, a shortening between the Si(Ge)-Si(Ge) distances is responsible for a change in the transition order from a first to a second one for x = 0.45. Also, the magnetic transition occurs at 290 K for this 0.45 composition nanostructure, see Fig.1(b), confirming the XRD analysis. Distinctly, for x = 0, the reduction to the nanometric scale leads to a superparamagnetic-like behavior that leads to a maximum of 8 J/kgK at 5 K that drastically reduces to null values as the temperature increases. Furthermore, the reduction of the unit cell volume was found to be directly related to the bulk target volumetric compressibility that is due to intrinsic surface tension (st) rising from the nanostructuring process. Thereby, we can conclude that the nanosecond PLD successfully produces dispersed crystalline nanoparticles of Gd5(Si1-xGex)4 family compounds. This technique allows the formation of NPs with particles size under 30 nm without loss on the stoichiometry of the targets, as observed through Synchrotron XRD [7]. Notwithstanding, the direct relation between bulk compressibility and nanoparticle size due to an intrinsic surface pressure might be the path to understand the particles' growth from pulsed laser deposition techniques under inert gas in the chamber.

**References:**

[1] V. K. Pecharsky and K. A: Gschneidner Jr., Phys. Rev. Lett., vol. 78, p. 4494 (1997); [2] L. Morellon, et al., Phys. Rev. B, vol. 58, p. R14721(R) (1998); [3] J. H. Belo, et al., J. of Mater. Res., vol. 34, p. 134 (2019); [4] R. L. Hadimani, et. al., Appl. Phys. Lett., v. 106, p. 032402 (2015); [5] J. H. Belo, et al., PRB, vol. 100, p. 134303 (2019); [6] N. Tarasenka, et al., J. Nanosci. Nanotechnol., vol. 16, p. 7451 (2016); [7] V. M. Andrade, et al., J. Alloys Compd., vol. 849, p. 156384 (2020[AP1] ).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/afe5422997f395a3795a6766687f1f04.jpg)
Figure 1: (a) TEM images for x = 0.45 nanoparticles with 27 nm of the mean size where the SAED reveals the good crystalline features of the structures. (b) Magnetic entropy change curves for all produced samples for an applied field of 5 T.

 Unit cell volume reduction of Gd5(Si,Ge)4 nanoparticles controlled by bulk compressibility

Faraday effect was a first demonstration of magnet influence on the light. Since then many generations of scientists tried to strengthen it. A decade ago, a breakthrough based on plasmonics was proposed for a significant enhancement of the magneto-optical interaction. However, all metals, even noble ones, introduce rather notable absorption which worsen quality factor of the optical resonances and constrains their role in the magneto-optical enhancement. Here we demonstrate that low lossy all-dielectric magnetic structures are more advantageous in this respect. We propose a specially designed all-dielectric magnetic meta-surface allowing a novel mechanism of the magneto-optical intensity effect [1]. It consists of a 2D array of iron-garnet nanopillars on an ultrathin iron-garnet slab. The nanostructure exhibits high transparency and superior quality-factor resonances followed by multifold increase of the magnetooptical intensity modulation. Unlike the magneto-optical intensity effects in smooth films and plasmonic gratings the photonic crystal metasurface provides the magnetically induced modulation of light intensity not only in a single light polarization, e.g. p-polarization, but also in the orthogonal one (s-polarization). It is due the wide variety of the excited mode types in the all-dielectric nanostructure. It is very promising for sensing, magnetometry and light modulation applications. This work was financially supported by the Russian Ministry of Education and Science, Megagrant project N 075-15-2019-1934.

**References:**

[1] D.O. Ignatyeva et al., Nature Communications 11, 5487 (2020).

**Images:**

 All-dielectric magnetophotonics INVITED

We present analysis of microscopic origin of magneto-optical spectra from the electronic structure of bcc Fe. The magneto-optical (MO) permittivity spectra are obtained by the WIEN2k code [1] and compared to the corresponding experimental MO Kerr effect spectra. The ab-initio spectra are given by the Kubo formula, i.e., as a result of summation over all pairs of electronic bands and integration over the Brillouin zone that all sum up to the single MO spectrum. We investigate what features of electronic structure contribute to the outgoing total MO spectrum. We have also developed several novel ways of visualizing MO-related phenomena in the Brillouin zone. It turns out that strong MO signal comes from several isolated k-points in the Brillouin zone, where the band degeneracy is avoided by the spin-orbit interaction (Fig.1). There are two major types of MO contributions determined by the nature of the avoided degeneracy (given by topology of the approaching bands), that contribute differently to the total MO spectrum. Both types are visualized and their contributions to the total spectrum are demonstrated in the form of local MO spectra. K-points, where the strong MO signal is originated, also give rise to strong Berry curvature. We show the flow of the Berry curvature in the vicinity of those k-points (Fig.2) and in the full Brillouin zone.

**References:**

[1] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka and J. Luitz, WIEN2k

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/89049a3a7102cf0d095032f0f6b7b2d8.jpg)
(a) Band structure of bcc Fe with colors corresponding to the d-character of bands with spin-up being positive and spin-dwon negative. (b) Joint band structure with colors representing the strength of the magneto-optical response. Strong magneto-optical transitions are marked by arrows and labelled by the corresponding band indices.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc6681d80eadbec89b015c676343ea08.jpg)
Flow of the Berry curvature in the vicinity of k-point with strong magneto-optical response.

 Magneto-Optical Effect in bcc Fe: Microscopic Origin and Topological Aspects

In the last decade, a huge amount of work has been devoted to constructing a composite thin film where magnetic anisotropy becomes tunable by coupling ferromagnetic layer to a functionalized layer. Electrical control of interfacial anisotropy with an insulator and interfacial strain transferred from an electrically controlled piezoelectric or ferroelectric material are still heavily pursued. In 2016, Feng et al. [1] proposed a novel approach to manipulate magnetic anisotropy by interfacial strain transferred from a thermally controlled NiTiNb shape memory alloy (SMA). They obtained pioneering results in showing small variation of interfacial anisotropy in NiTiNb (0.5mm)/FePt (10–20 nm) with in-plane anisotropy. This innovative architecture benefits from the shape memory effect, in particular, from the two-way shape memory effect (TWSME). The TWSME consists in a reproducible hysteretic transformation of shape memory alloys from a strained B19’ structure (at low temperature) to a differently strained B2 structure (at high temperature) during the thermal cycle. NiTi-based alloys are among the most used shape memory alloys within a wide range of applications in industry, military technologies, health care, etc. [2]. They are metallic and may be grown by regular microelectronics industry deposition techniques. NiTi-based SMAs can produce as much as 4% of TWSME strain and recover up to 10% of the initial deformation [3]. The transformation temperatures can be easily tuned from 250 K to 1000 K [2]. In our talk, we demonstrate that the NiTi alloy can be used to reproducibly switch by 90° the in-plane uniaxial anisotropy of a 20 nm thick Ni thin film during a thermal cycle between room temperature and 100°C (as shown in Figure 1) [4]. We first properly quantify NiTi sample longitudinal strain and transverse strain produced by an external uniaxial tensile stress followed by a thermal cycle, required to setup the TWSME. We demonstrate that NiTi is a Pauli paramagnetic material and explain temperature variations of its magnetic susceptibility by comparing experimental data with ab-initio calculations [5]. We show that both martensitic transition temperature and magnetic susceptibility depend on NiTi lattice structure, which we tuned through strain and characterized by TEM and XRD techniques. Secondly, we characterize magnetic anisotropy of the Ni layer, deposited by PVD on top of NiTi after tensile deformation. As shown in Fig. 1, when NiTi is in its martensite (respectively, austenite) phase, Ni anisotropy points along (respectively, perpendicular to) the initial tensile axis. Variation of Ni anisotropy up to 1.105 J.m-3 was achieved. It is a promising result since the strain transfer at NiTi/Ni interface is not yet optimized. Indeed during the TWSME strain in NiTi varies from 0% to 2.7% whereas Ni strain varies only from 0% to 1.3. We performed transmission electron microscopy and reveal that a thin oxidized interface layer is the main origin of strain loss at the NiTi/Ni interface.

**References:**

[1] C. Feng et al., Appl. Phys. Lett. 109, 212401 (2016) [2] J. Mohd Jani, et al., Mater. Des. (1980–2015) 56, 1078 (2014) [3] O. Benafan, et al., J. Appl. Phys. 112, 093510 (2012) [4] A. Kyianytsia et al., Appl. Phys. Lett. 115, 222402 (2019) [5] A. Kyianytsia et al., Appl. Phys. Lett. 117, 122411 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c19037b2f749a5e8b58c235308b7d528.jpg)
(a–b) Magnetization vs magnetic field when the field is applied along the x-axis (0°), and y-axis (90°), when NiTi is in martensite state (E state) and austenite state (F state). (c) Remanent magnetization of NiTi/Ni as a function of magnetic field angle for E and F state.

 Magnetic anisotropy switching induced by shape memory effect in NiTi/Ni bilayer

High-temperature shape memory alloys (HT-SMAs) are required in specific automotive, aerospace or energy applications [1], [2]. Common binary Ni-Ti SMAs are characterized by a limited transformation temperature and, thus, cannot be used for applications operating at 100°C or above. Ternary elements (Pt, Au, Hf, Zr) can be added to increase the transformation temperature [3]. The ternary Ni-Ti-Hf alloy is currently the most promising candidate material, however, pronounced brittleness and high costs due to the significant amount of Hf hinders its technological breakthrough. Alternative HT-SMAs are Co-Ni-Ga Heusler alloys. These materials undergo a first-order magnetostructural transformation (FOMST) from high-temperature B2-ordered austenite to tetragonal L10 low-temperature martensite [4]. A fully reversible superelastic response up to 500°C as well as excellent cyclic stability up to temperatures of 100°C have been reported for single-crystals [5]. However, polycrystalline Co-Ni-Ga suffers from intergranular cracking and a premature failure after several transformation cycles due to the anisotropic volume change of randomly crystallographic orientated grains. Many efforts in the fields of grain boundary and microstructure engineering have been done to synthesize HT-SMAs with favorable grain boundary configuration in order to fully prevent intergranular cracking and premature failure. It was reported that a columnar-grained microstructure with strong &lt;001&gt; texture and straight low-angle grain boundaries can overcome the structural and functional limitations in Cu-based SMAs [6]. Additive manufacturing (AM) is a very promising technique to synthesize HT-SMA since it allows a direct microstructure design. Selective laser melting (SLM) and directed energy deposition (DED) are two common AM techniques for metallic alloys. During the SLM process, pre-alloyed powder is molten layer-by-layer using a laser system operating under inert gas atmosphere to prevent oxidation. Microstructure can be directly tailored by different processing parameters like laser power, scanning velocity and scanning path. In contrast to the powder-bed based SLM, DED is a powder-stream based process using nozzles to directly transfer the powder material into a focused laser beam. Similar to the SLM process the microstructure can be directly tailored by varying the processing parameters such as laser power and scanning speed. In our present work, we compare the microstructure and magnetic properties of Co49Ni21Ga30 alloys processed by SLM and DED with single crystals as well as polycrystalline material prepared by conventional casting. The preferred columnar-grained microstructure could be obtained by proper choice of processing parameters for the different AM techniques [7], [8]. Fig. 1 shows the microstructure of Co-Ni-Ga fabricated by SLM. The electron backscatter diffraction (EBSD) analysis of the cross-section shows a polycrystalline columnar-grained microstructure along the building direction (BD) [7]. A similar columnar-grained microstructure is also observed in the DED processed material [8]. In addition, the DED sample is characterized by a strong &lt;001&gt; texture along BD. Due to these highly anisotropic microstructures, AM processed Co-Ni-Ga obtained by both, SLM and DED, shows excellent HT-SMA properties without any post-processing [7], [8]. To study the FOMST in more detail, temperature and field-dependent magnetization measurements were performed. Fig. 2 shows the temperature-dependent magnetization of additively processed samples, polycrystalline material in the as-cast condition and in a single crystalline state for different orientations. The SLM sample reveals the largest transition width and thermal hysteresis while the DED sample provides for a transformation behavior being very similar to the cast and single crystalline counterparts. Since the transformation behavior depends on parameters such as grain size, residual stresses, defects and precipitates [9] the influence of the processing parameters on these parameters is essential to understand the FOMST and functional properties in Co-Ni-Ga in more detail. This work was supported by the ERC Advanced Grant "CoolInnov" (No 743116), the CRC/TRR 270 “HoMMage” (DFG). TN acknowledges funding by DFG (No 398899207).

**References:**

[1] J. Ma, I. Karaman, R. D. Noebe, International Materials Reviews, vol. 55, pp. 257-315, (2010) [2] K. Otsuka, Ed., Shape memory materials, Cambridge Univ. Press, (1999) [3] M. Elahinia et al., Scripta Materialia, vol. 145, pp. 90-94, (2018) [4] A. Reul et al., Shap. Mem. Superelasticity, vol. 4, pp. 61-69, (2018) [5] P. Krooß et al., Shap. Mem. Superelasticity, vol. 1, pp. 6-17, (2015) [6] J.-L. Liu, H.-Y. Huang, J.-X. Xie, Materials & Design, vol. 64, pp. 427-433, (2014) [7] C. Lauhoff et al., Metall and Mat Trans A, vol. 51, pp. 1056-1061, (2020) [8] C. Lauhoff et al., Materials Research Letters, vol. 8, pp. 314-320, (2020) [9] F. Scheibel et al., Energy Technol., vol. 6, pp. 1397-1428, (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/237965b772da9e5c7d95872cd06b33fe.jpg)
Fig. 1: Microstructure of Co-Ni-Ga processed by SLM: (a) optical micrograph, the building direction is perpendicular to the surface, (b) EBSD inverse pole figure map of the cross-section revealing a polycrystalline columnar-grained microstructure along the building direction (BD)

![](https://assets.underline.io/uploads/markdown_image/1/image/ca9914c1650bb2f6243d137454ae4bf8.jpg)
Fig. 2: Temperature dependent magnetization of (a) Co-Ni-Ga single crystals, (b) cast polycrystalline Co-Ni-Ga and Co-Ni-Ga alloy processed by SLM and DED.

 Influence of additive manufacturing processes on the microstructure and magnetic properties of Co-Ni-Ga shape memory Heusler alloy

Recent progress in multiferroic antenna shows high promise for communication in rf-denied environment for transmitting signals in lossy electrically conductive media. The antenna utilizes the ultra-low (ULF/VLF) frequency band (1 – 30 kHz) while also maintaining a compact design [1]. In such multiferroic antennas, containing magnetostictive materials that are mechanically actuated, becoming a near-field magnetic field transmitter. This transduction mechanism is based on magnetization changes inside the magnetostrictive material, due to the application of time-variable stresses generated by an electrically-driven piezoelectric material (which is elastically coupled with the magnetostrictor). Magnetoelectric coupling between the piezoelectric driving element and magnetostrictive material allows for modulation of a large magnetic signal form the multiferroic antenna [2]. Of particular importance is the material with a high piezomagnetic coefficient coupled with a large change in the internal flux density. Iron-gallium alloys, Fe1-xGax (Galfenol) with 0.12 &lt; x &lt; 0.30, are promising magnetostrictive, transducer materials that combine highly desirable tensile and compressive mechanical excitation with superior magnetic properties [3]. Doping studies of Galfenol show a maximum in the magnetostrictive response when the Ga composition is x = 0 16 – 0.19; while there is an additional peak at higher gallium compositions, this range maintains a large internal flux response [3,4]. This work investigates the mechanically-driven magnetic response of several Galfenol compositions as a function of driving frequency. A solid and laminated rod of similar size are also compared to determine the effect of eddy current losses on the flux response of the rod. The laminated rod is composed of 12 μm, epoxy bonded Galfenol sheets with x = 0.186. Magnetostrictive transducer elements under test were placed in a nonmagnetic frame with an applied, axial static prestress and permanent magnets placed above the Galfenol rods. When placed in an optimal magnetic bias field and compressively actuated through driving with a Pb[Zr,Ti]O3 (PZT) stack the magnetostrictive Galfenol changes magnetic states depending upon the applied stress. The bias magnetic field was optimized by determining the distance where the permanent magnets would allow for the highest Galfenol flux density response. A fluxgate magnetometer at 1 m and search coil surrounding the Galfenol rods determined the radiated magnetic field and changing internal flux, respectively; both showed similar frequency responses. Figure 1 shows the near-field (1 m) response of 3 samples (2 solid rods and 1 laminated) revealing an improved response at the lower Ga composition. Interestingly, a larger signal was measured from the laminated sample at all frequencies despite being a higher composition (18.4 at. % Ga); it also showed little variation with increasing frequency over the measured range. The laminated sample showed better operational properties compared with the solid samples that decreased with increasing frequency. Mechanically driven laminated Galfenol samples showed an improved dynamic response when compared with solid rods. Additional optimizations to the device configuration are possible as variations in production quality, heat treatments, and microstructural properties such as grain size and domain boundaries can affect the magnetostrictive and magnetic response of the material. Further investigations are needed to verify if any additional improvements are possible through annealing.

**References:**

[1] Joseph D. Schneider, John P. Domann, and Gregory P. Carman, Journal of Applied Physics 126, 224104 (2019) [2] Junran Xu, Chung Ming Leung, and Dwight Viehland, Sensors, 19(4), 853 (2019) [3] G. Petculescu, K. B. Hathaway, and A. E. Clark, Journal of Applied Physics 97, 10M315 (2005) [4] A. Mahadevan, P. G. Evans, and M. J. Dapinoa, Appl. Phys. Lett. 96, 012502 (2010)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/edccf778d2f230d28c475ab79dc55641.jpg)
Figure 1: Frequency response of the fluxgate magnetometer 1 meter from the actuated Galfenol rods (solid: 17 and 18 at. % Ga; laminated: 18.4 at. % Ga), showing a nearly flat frequency response for the laminated rod from 300Hz to 2kHz. Both solid rods decrease with increasing frequency. The 18% solid rod has been annealed under tension.

 Dynamic response of Fe-Ga for multiferroic magnetic field transmitters

The paper presents the steps that brought the authors to design and implement the proof of principle of a fuel injector based on a custom Terfenol-D actuator. Magnetostrictive actuators play a relevant role in the perception of usefulness of smart materials and devices. Their applications are potentially wider than that of piezoelectric actuators because of the higher energy density and intrinsic robustness [1]. This activity is aimed to investigate the basic elements related to the fuel injection by fully controlling the injection rate. This would contribute to the NOx emission reduction that is a crucial goal for internal combustion engines. The study provides the design, development and a feasibility analysis of a magnetostrictive actuator for fuel injection, by providing both magneto-static numerical analysis of the actuator, the adaptation of a commercial fuel injector and its final experimental testing. Commercial fuel injectors work under on/off conditions and the modulation of the fuel rate is made over time. Recent developments make use of piezo-stacks to control the fuel injector needle [2] but the system is rather complex because the piezo-stacks cannot directly withstand the fuel high pressures. Indeed, the use of magnetostrictive materials would allow to have a simpler device with a full direct control of the injection and with higher achievable injection pressures [3]. The first step in the proof of principle has been the accurate design and analysis of the actuator employing a Terfenol-D magnetostrictive alloy aimed for the needle driving of a commercial fuel diesel injector with hydraulic drive. To this aim, a custom actuator employing a magnetostrictive alloy and fulfilling reasonable constraints for fuel injection (needle Lift of 50 - 200 μm, injection Pressure of 250-1000 bar, rise Time of 100 μs and a duty Cicle of 1/20 ms/ms) has been designed. The scheme of the magnetostrictive actuator, mechanically coupled with the modified injector, is shown in Fig. 1-left. The mechanical frame is acting also as a magnetic circuit and can accommodate different magnetostrictive rods. It is equipped with embedded force and displacement force sensors. The Fig. 1-right shows the realized prototype ready for injection tests. The magnetic circuit includes permanent magnets aimed to provide a bias magnetic field able to force the MS rods to the maximum stroke at zero current in the coil. In this condition the injector’s holes are closed at zero current. The coil is designed to reduce magnetization in the rod driving back the needle and allowing the fuel injection. The system has been assembled and successfully tested with different driving signals. The Fig.2 shows the trigger signal (A), needle displacement (B), flow rate (C) and coil current (D) in case of square (red curves) and triangular (black curves) references and it is apparent that the flow rate sufficiently follows the reference signal shape. In the complete paper more details about the design, the numerical analysis and the experimental tests will be given.

**References:**

[1] Apicella, V.; Clemente, C.S.; Davino, D.; Leone, D.; Visone, C. Review of Modeling and Control of Magnetostrictive Actuators. Actuators 2019, 8, 45. [2] H. Nouraei, R. Ben-Mrad and A. N. Sinclair, Development of a Piezoelectric Fuel Injector, IEEE Transactions on Vehicular Technology, 65(3),1162-1170, 2016, doi: 10.1109/TVT.2015.2410136. [3] G. Xue et al, A review of giant magnetostrictive injector (GMI), Sensors and Actuators A: Physical, 273 (2018), 159-181, https://doi.org/10.1016/j.sna.2018.02.001.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3c13ab81c3773b95c2eb5a9ba9ebdcdf.jpg)
Fig.1: Scheme of the custom actuator (left) and of the assembled prototype (right).

![](https://assets.underline.io/uploads/markdown_image/1/image/d0cdb6c26116660b98d6714072534796.jpg)
Fig.2: Reference signal (A), needle displacement (B), flow rate (C) and coil current (D) in case of square (red curves) and triangular (black curves) references at a 500-bar injection pressure.

Validation of a Reduced Order Magnetoelastic Beam Model

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