France



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, Δ&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;iso&lt;/sub&gt;) and inverse MCE (negative Δ&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;iso&lt;/sub&gt;). 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.&lt;br/&gt;&lt;br/&gt;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 Ni&lt;sub&gt;48.1&lt;/sub&gt;Mn&lt;sub&gt;36.5&lt;/sub&gt;In&lt;sub&gt;15.4 &lt;/sub&gt;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 Δ&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;iso&lt;/sub&gt; 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 Δ&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;iso&lt;/sub&gt; 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:&lt;br/&gt;&lt;br/&gt;- Universal scaling can be used to deconvolute overlapping first and second order phase transitions.&lt;br/&gt;&lt;br/&gt;- The broadening of the SOPT with increasing field causes a larger overlap between transitions despite the shift of the FOPT to lower temperatures.&lt;br/&gt;&lt;br/&gt;- 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.&lt;br/&gt;&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;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.&lt;br/&gt;[2] J. Y. Law, Á. Díaz-García, L. M. Moreno-Ramírez, V. Franco, A. Conde, A. K. Giri, Acta Mater. 166 (2019) 459.&lt;br/&gt;[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 Δ&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;iso&lt;/sub&gt; of Ni&lt;sub&gt;48.1&lt;/sub&gt;Mn&lt;sub&gt;36.5&lt;/sub&gt;In&lt;sub&gt;15.4&lt;/sub&gt; Heusler alloy for different magnetic fields (open symbols) and its reconstructed Δ&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;iso &lt;/sub&gt;response (stars symbols). (Bottom panel) Temperature dependence of Δ&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;iso&lt;/sub&gt; for different fields of the deconvoluted responses of the SOPT (open symbols) and the FOPT (solid symbols).



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

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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).

technical paper

Nowadays multi-material additive manufacturing (AM) is attracting much interest in many high technological sectors such as automotive, energy, electronics, aeronautics and medicine. The combination of AM technology with the synthesis of composite materials allows for designing and fabricating objects with complex shapes and tuned properties for reaching high performance [1]. For permanent magnet (PM) applications, a present challenge is developing magnets by AM with no geometrical constrictions, high filling factor (FF) to avoid diluting their magnetic properties, and no deterioration of their PM properties during processing [2]. The industrial fabrication of PM/polymer composites (typically in the shape of pellets) is done by mechanical methods. We showed recently, and for the very first time, the possibility of producing a continuous PM-based filament (meters long) using as a precursor a highly loaded PM/polymer composite synthesized by solution casting [3]. This technique allows for the synthesis of customized composites making possible the choice of the polymer according to the requirements dictated by the final application. Moreover, it is an easily scalable route, which opens a new path to the AM technology of PMs. In this study, different composites (PM particles/polymer) have been analyzed consisting on several PM materials: gas-atomized τ-MnAlC (Fig. 1(a)), Sr-ferrite, NdFeB, and hybrid (NdFeB/Sr-ferrite) powders embedded in different polymer matrix. It is of large scientific and technological interest to consider rare earth (RE)-free PM alternatives such as improved ferrites, and the promising MnAl-based alloys [4]. The starting powders showed different mean particle size ranging from the 5 μm of Sr-ferrite to the 50 μm of NdFeB powders. MnAlC powders showed an intermediate mean particle size between 15 and 30 μm. This work will show the effect of particle size (with special attention to the benefits of combining dissimilar sizes), polymer and fabrication parameters on the properties of the final products, showing that they are key factors to be considered and optimized for obtaining flexible and continuous filaments with a high FF. Particle size plays a key role when extruding the composites in order to obtain flexible filaments with a high FF [3,5,6]. It has been observed that if the mean particle size is larger than 20 μm (coarse particles), the extrusion process is affected by the composite rheology under the exerted pressures and, consequently, the FF of the extruded filament is reduced [5,6]. A key result from this study is the demonstration that, by mixing particles with different size and optimizing the fine-to-coarse particles ratio, it is possible to obtain flexible filaments with increased FF (up to 90%), i.e., leading to an enhanced effectiveness of the extrusion process [5,6]. MnAlC-based composites were synthesized by solution casting (Fig. 1(a)) making possible to tune the FF, reaching extremely high values above 85% [3]. Composites were extruded into continuous and flexible filaments with PM properties (Fig. 1(b)), with a length over 10 m [3,6]. The homogeneity of the composites and filaments has been determined by scanning electron microscopy, SEM (Fig. 1(b)). Processing of SEM images allowed for obtaining the FF of the composites and filaments. Vibrating sample magnetometry (VSM) has been used for accurately determining the FF of composites and filaments, being positioned as a faster technique in comparison with image processing. Moreover, and important in view of practical applications, this technique has demonstrated the no deterioration of PM properties of the starting particles after composite synthesis and filament extrusion processes (Fig. 1(b)) [3,5,6]. We will compare these results with those obtained in the preparation of filament prepared from composites based on: Sr-ferrite (Hc~3 kOe, FF=92%), NdFeB (Hc=10.2 kOe, FF=83%) and hybrid composites containing fine (Sr-ferrite) and coarse (NdFeB) particles (Hc=8 kOe, FF=90%). Optimized MnAlC-based filament (with a high MnAlC content above 80 wt.%) was used for 3D-printing objects as a proof-of-concept (Fig. 2). Magnetic measurements performed on the printed objects (Fig. 2) have proved that alternative PM materials can be efficiently synthesized and processed for developing novel PMs by AM under controlled processing temperature, which might be used in sensing devices [6]. Acknowledgements Authors acknowledge fruitful collaboration and discussions with B. Skårman, H. Vidarsson and P.-O. Larsson from Höganäs AB (Sweden), and A. Nieto and R. Altimira from IMA S.L.U. (Spain). Authors additionally acknowledge financial support from EU M-ERA.NET and MINECO through the projects "NEXMAG" (M-ERA.NET Project Success Case, Ref. PCIN-2015-126) and "3D-MAGNETOH" (Ref. MAT2017-89960-R); Regional Government of Madrid through "NANOMAGCOST" project (Ref. P2018/NMT-4321); and Höganäs AB through the industrial contract "GAMMA".

**References:**

[1] S.A.M. Tofail et al., Mater. Today, 21, 22 (2018) [2] C. Huber et al., Appl. Phys. Lett., 109, 162401 (2016) [3] E.M. Palmero et al., Sci. Technol. Adv. Mater., 19, 465 (2018) [4] A. Bollero et al., ACS Sustainable Chem. Eng., 5, 3243 (2017); J. Rial et al., Acta Mater., 157, 42 (2018); J. Rial et al. Engineering, 6 (2), 173; C. Muñoz-Rodríguez et al., J. Alloys Compd., 847, 156361 (2020) [5] E.M. Palmero et al., IEEE Trans. Magn., 55, 2101004 (2019) [6] E.M. Palmero et al., Addit. Manuf., 33, 101179 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/07242cdfa3f27df187acf728ebcc1b22.jpg)
Fig. 1. (a) Composite synthesis by solution casting with representative images of the starting MnAlC powders and the resulting MnAlC/polymer composite. (b) Second quadrant of the hysteresis loops measured at room temperature for the gas-atomized MnAlC particles, MnAlC/polymer composite and extruded filament. Inset shows an extruded MnAlC-based filament together with an SEM image of its circular cross section.

![](https://assets.underline.io/uploads/markdown_image/1/image/313f4a31e639429f97217f5044912754.jpg)
Fig. 2. Magnetic pieces obtained by additive manufacturing using an extruded filament based on MnAlC particles, together with the magnetic flux density measured at the surface of a 3D-printed disc.

 Additive Manufacturing of Rare Earth-free and Hybrid Permanent Magnets: from Composites synthesized by Solution Casting to Magnetic Filament and 3D-printing of Magnets

Permanent magnets are receiving an increasing economical impact due to their role in the Low Carbon Green Transition being employed for energy generation (wind generators), energy storage (flywheels) and electric transport. However, the most performing magnets, composed by rare earth (RE) elements, are in the head of the list of the Critical Raw Materials due to the recent uncertainty in supply and the increase of the costs of the RE. This last question has pushed the research of alternatives to RE magnets. Between the different solutions, the improvement of the performances of the hard ferrites is receiving an increasing interest [1-4]. In fact, ferrite magnets constitute by far the most widely used permanent magnet by weight [2,3] and any improvement of the performances is expected to have an important impact [4]. The most promising approach to improve the performances of ferrite magnets is the development of nanocomposites formed by magnetically coupled high magnetization and hard magnetic nanophases [4]. We present a research on a novel class of hybrid magnet composed by micrometric nanowires (NWs) and micrometric ferrites that exhibit improved hard magnetic properties. We have investigated the properties of composites containing micrometric FeCo nanowires and micrometric SrFe12O19 powders [5] to produce bonded magnets. FeCo NWs were prepared by template-assisted electrochemical deposition using nanoporous templates and polycarbonate nanoporous membranes to obtain NWs with different diameters (30, 50, and 100 nm). FeCo NWs−strontium ferrite mixture composites in the powder form were fabricated by mixing each phase. The evolution of the magnetic properties of the mixtures considering the different diameter of the NWs and the soft-hard ratio will be shown. The coercive field of the composites decreases as the soft contain is larger, while remanence magnetization remains almost constant but also increases depending on NWs size. The magnetic coupling between the two phases has been investigated using remanence measurements. Even the soft nature of the NWs, the hard and soft phases are magnetically coupled up to a 20%wt of the soft phase in the case of the NWs of 50 nm of diameter. A 20% increase in remanence together with a weak decrease in coercivity, as consequence of the magnetodipolar interaction between ferrite particles and FeCo NWs, is observed. In fact, the oriented bonded composites magnets exhibit a larger energy product up to 40% larger than the corresponding ferrite ones. The magnetic properties of these magnets will be discussed considering the magnetic configuration of the Nanowires. This research was supported by EU- H2020 AMPHIBIAN Project (H2020-NMBP-2016-720853) and by the JECS Trust.

**References:**

[1] EU-H2020, AMPHIBIAN Project. Website : amphibianproject.eu. [2] R. C. Pullar, Progress in Materials Science 57, 1191 (2012). [3] S H Mahmood and I Abu-Aljarayesh Hexaferrite Permanent Magnetic Materials. Materials Research Forum LLC, (2016) [4] C. de Julián Fernández et al., J. Applied Phys. D: Applied Physics, (2020) in press

**Images:**

 Metal Nanowire−Strontium Ferrite Composites for Free Rare-Earth Magnets

The design and development of alloys are typically based on one or two main constituents since the Bronze age, whereby the search for new materials using this millennia-old technique is reaching limits. Today, a new class of materials, using a different design approach of alloying multiple elements (five or more) to form compositions without dominant elements and therefore having high entropy of mixing, can discover materials with excellent properties, some of them being superior or unique compared to the conventional materials. This is also known as the high-entropy alloy (HEA) design concept where its multi-principal-element composition encompasses a vast compositional space, which further indicates many opportunities for materials design. While HEA research expands at a rapid growth since its first report in 2004 and has evolved from 1st to 2nd generation HEAs, most of the efforts focus on structural applications while their functional reports are scarce in comparison to their mechanical properties. Furthermore, when compared to conventional functional materials, they underperform due to their modest functional properties. One of their most reported functional properties, the magnetocaloric effect (MCE), only shows large values among HEAs for those compositions containing rare-earth elements. The rare-earth-free HEAs, on the other hand, typically exhibit very small MCE instead. In this talk, we will show that it is possible to enhance the MCE of rare-earth-free HEAs by at least one order of magnitude upon introducing a magneto-structural phase transition: isothermal entropy change increases from 1.7 to 13.1 J kg-1 K-1 (for 2.5 T) [1,2]. The significant improvement in the MCE performance is further shown in Fig. 1 when comparing the isothermal entropy change and the temperature averaged entropy change, TEC(10), to the literature. Instead of sampling the huge HEA compositional space by brute force, we have followed a directed search procedure to develop FeMnNiGexSi1-x HEAs that enabled us to put the functionality of HEAs comparable to some of the high-performance traditional materials. The variation of Ge/Si ratio enables the tuning of the thermomagnetic phase transitions (magneto-structural transformation and Curie transitions), leading to a further enhancement in the MCE. Our work is also found to merge the gap between magnetocaloric HEAs versus conventional magnetocaloric materials. These findings demonstrate the promising potential of HEAs for magnetocaloric applications. 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.

**References:**

[1] J.Y. Law, L.M. Moreno-Ramírez, Á. Díaz-García, A. Martín-Cid, S. Kobayashi, S. Kawaguchi, T. Nakamura, V. Franco, J. Alloy. Compd. 855 pp. 157424 (2021) . [2] J.Y. Law, Á. Díaz-García, L.M. Moreno-Ramírez, V. Franco, Submitted (2021). [3] M.C. Gao, D.B. Miracle, D. Maurice, X. Yan, Y. Zhang, J.A. Hawk, J. Mater. Res. 33(19) pp.3138-3155 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c0853824f7a3d0b587ae32052421cf30.png)
Fig 1. Performance comparison of magnetocaloric HEAs for 2.5 T based on isothermal entropy change peak, its corresponding temperature and temperature averaged entropy change over a 10 K span, TEC(10). Each data point represents a single material, with a diameter size proportional to its TEC(10). Literature data are collected from refs. [1 - 3].

 Overcoming the Limitations of Magnetocaloric Rare-Earth-Free High-Entropy Alloys INVITED

In the age of climate change and the global goal of reducing CO2 emissions, the increase of energy efficiency becomes an important aspect of material and device development in many industrial sectors. The energy spent for cooling and air conditioning in industry and households represents a significant part of the global energy consumption. Furthermore, it is predicted that the amount of energy needed for cooling will rise drastically within this century [1]. Magnetocaloric (MC) refrigeration attracts a lot of attention since it can be more energy efficient and environmentally friendly than current vapor compression technology [2]. It uses a solid-state magnetic material that heats up and cools down cyclically when exposed to a changing magnetic field. Many efforts are guided towards a reduction of the thermal hysteresis to enhance the cyclic magnetocaloric effect (MCE) in first-order materials [3]. An alternative solution has been proposed, which benefits from the thermal hysteresis by using two stimuli to trigger the phase transition in a multicaloric material [4]. In a first step, the application of a magnetic field induces the high-magnetization state which leads to a negative adiabatic temperature change for the case of an inverse MC material. The large thermal hysteresis prevents the back transformation and locks the material in its high-magnetization phase, which allows an efficient heat exchange in zero field. In order to transform the material back, an external stress is applied as a second stimulus leading to a conventional elastocaloric effect (ECE). The use of two stimuli enables a complete first-order transformation under cyclic conditions. Therefore, the drawback of the thermal hysteresis which limits the cyclic performance in a MC cycle can be overcome by using a second stimulus. Furthermore, the amount of permanent magnets to generate the magnetic field can be significantly reduced in a multi-stimuli cycle because the material needs to be magnetized only for a short time and in a small volume. The caloric material for the new multi-stimuli cycle requires a large sensitivity of the phase transition towards both stimuli as well as a good mechanical stability. In this work, we present the concept of the new multi-stimuli cooling concept including potential material systems and methods to tailor their functional and mechanical properties. The main objective is adapting the properties for a classical MC cycle towards the extended needs of the multi-stimuli cycle and tailoring the desired properties by intrinsic and extrinsic means. The most promising materials are Ni-(Co)-Mn-based Heusler alloy due to their adjustable transition temperature and large MCE [5]. We studied these alloy systems with respect to their MC response in low and high magnetic fields as well as for varying field-sweep rates. For the second applied stimulus, the behavior under uniaxial stress application has been investigated for arc-molten and suction-cast alloys. The influence of microstructural modifications, such as grain refinement and precipitates, were studied regarding mechanical stability and caloric performance. Especially the microstructure has an influence on the thermal hysteresis and caloric functionality. Thus, we studied the possibility of tailoring the thermal hysteresis as well as improving the mechanical stability by the addition of secondary phases. We could show that the doping with Gd introduces Gd-rich precipitates into a Ni-(Co)-Mn-In matrix. The alloy shows a magnetic entropy change of 9 Jkg-1K-1 and an adiabatic temperature change of 4 K in 2 T, comparable with values for phase-pure Ni-Mn-In alloys. Compression tests show that the strength is increased significantly for samples with Gd-rich precipitates. In parallel, the development of new Heusler systems opened up broad perspectives since the realization of all-d-Heusler alloys [6]. Recently, the system of Ni-Co-Mn-Ti is investigated intensively because of large MCE and good mechanical properties for a single-phase microstructure. In addition, a large volume change during the martensitic phase transition leads to a large ECE. By optimizing the heat treatment, we could enhance the sharpness of the phase transition and reach large isothermal entropy changes of up to 40 Jkg-1K-1 in 2 T [7]. A systematic study of different Co- and Ti-contents results in a phase diagram, from which the transition temperature can be estimated by the e/a ratio. In addition, the magnetic-field-sensitivity as well as the stress-sensitivity of the phase transition and the thermal hysteresis can be designed precisely by tuning the stoichiometry. The mechanical stability required for a cyclic application of stress can be tailored by the microstructure, e.g. by variation of the processing route. In order to evaluate general design rules for magnetocaloric compounds, the novel all-d Heusler system is compared to the well-characterized Ni-Mn-X alloys with X being a main group element. Significant differences could be attributed to the preferred state of atomic order, which has been analysed by combining the experimental results with theoretical calculations. This work was supported by the ERC Advanced Grant "CoolInnov" (No 743116), and the CRC/TRR 270 “HoMMage” (DFG).

**References:**

[1] M. Isaac, D. P. van Vuuren, Energy Policy 37, 507 (2009) [2] O. Gutfleisch et al., Adv. Mater. 23, 821-842 (2011) [3] F. Scheibel et al., Energy Technol. 6, 1397-1428 (2018) [4] T. Gottschall et al., Nature Mat. 17, 929-934 (2018) [5] A. Taubel et al., Phys. Status Solidi B 255, 1700331 (2018) [5] Z. Y. Wei et al., Appl. Phys. Lett. 107, 022406 (2015) [6] A. Taubel et al., Acta Mater. 201, 425-434 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7435144c2cb405ced22b83f1c2045ae1.jpg)
Schematic of the six-step multi-stimuli cycle, which makes use of a large thermal hysteresis [4].

![](https://assets.underline.io/uploads/markdown_image/1/image/67235d93137d710950d00008a4b37bf2.jpg)
Tailoring the functional properties of Ni-Co-Mn-Ti by varying the stoichiometry (a) and tuning mechanical properties of Ni-Mn-In by introducing secondary phases (b).

 Designing multicaloric materials for using thermal hysteresis in a novel multi-stimuli cooling cycle

Solid-state cooling devices based on the “caloric” class of functional materials are considered a promising alternative to conventional vapor compression technologies as they allow complete elimination of high-global warming potential (GWP) refrigerants and have high energy efficiency that is theoretically equivalent to 60% of Carnot efficiency. [1] By definition, multicaloric materials exhibit reversible thermal changes that can be driven concurrently or in sequence by more than one type of external energy sources (magnetic field, electric field, strain/pressure). The use of multiple driving forces can bring about larger thermal changes with smaller field magnitudes over broader operating temperature ranges, while reducing energy losses due to hysteresis in one control parameter by shifting it to another. Multicaloric materials under current investigation are fraught with issues related to the inclusion of strategically-limited and toxic elements (e.g., Gd5(GeSi)4, FeRh, MnAs; bold=problematic element) or require complex synthesis and processing to realize an acceptable, or even marginal, functional response. Against this backdrop, the MnTX family of compounds [T = transition metal elements (Fe, Ni, or Co); X= main group p-block element (Si, Ge, or Sn] are poised to overcome these limitations since they are made of earth-abundant, non-toxic elements, are scalable for powder production using low-cost, conventional solid-state processing techniques. Select MnTX alloys demonstrate tunable, room-temperature, first-order magnetic phase transition (i.e., magnetostructural transition from a low temperature TiNiSi-type ferromagnetic orthorhombic phase to a high temperature Ni2In-type paramagnetic hexagonal phase) with promising magnetic fields and pressure-driven caloric responses. Though one can tune the magnetic and caloric properties through careful choice of chemical elements that occupy T- and X-sites or their relative concentrations, large chemical diversity presents formidable combinatorial challenges for experimental and theoretical studies. To accelerate the discovery of new MnTX materials with low hysteresis magneto-structural phase transitions near room temperature, we apply a machine learning (ML) approach utilizing data from published literature to construct data-driven ML models as illustrated in figure one. To this end, we start by performing a literature review and constructing a database representative of the MnTX materials that undergo the Pnma to P63/mmc magneto-structural transition. [2]-[21] We found 87 unique observations that have been experimentally synthesized and whose Pnma to P63/mmc transition temperature on heating (TH) and P63/mmc to Pnma transition temperature on cooling (TC) have been characterized. The difference between |TH – TC| is indicative of the hysteresis associated with the phase transition. From these 87 observations, we created 2 different methods of representing the data for machine learning. The first was created using element specific features (e.g., valence electron concentration, electronegativity, and size), where each composition is described as a weighted average of these individual elemental properties. In the second method, we performed density functional theory (DFT) to calculate certain properties (e.g., magnetic moment, bond lengths, and unit cell parameters) of end-point compositions for each compound using the open source electronic structure code quantum espresso.[22]–[24] Each alloy or solid solution was then described as a weighted average of the properties of each end point composition. Models were trained using bootstrapped LASSO, support vector regression (SVR), gaussian process regression and random forest methods implanted in the statistical computing language, R.[25] Of these algorithms SVR was the most accurate on the validation set for both the elemental feature space and the DFT feature space. The perfomance of this model is shown in figure two. When compared to each other the model trained on the DFT generated features out-performed the model trained on the features generated from elemental properties. Promising candidates are recommended for experimental validation and feedback for iterative model improvement.

**References:**

[1] J. Lyubina, “Magnetocaloric materials for energy efficient cooling,” Journal of Physics D: Applied Physics. 2017, doi: 10.1088/1361-6463/50/5/053002. [2] A. Biswas et al., “Designed materials with the giant magnetocaloric effect near room temperature,” Acta Mater., 2019, doi: 10.1016/j.actamat.2019.09.023. [3] J. H. Chen et al., “Tuning martensitic transitions in (MnNiSi)0.65(Fe2Ge)0.35 through heat treatment and hydrostatic pressure,” J. Appl. Phys., 2018, doi: 10.1063/1.5051551. [4] J. Liu et al., “Realization of magnetostructural coupling by modifying structural transitions in MnNiSi-CoNiGe system with a wide Curie-temperature window,” Sci. Rep., 2016, doi: 10.1038/srep23386. [5] P. Lloveras et al., “Giant reversible barocaloric response of (MnNiSi)1- x(FeCoGe)x (x = 0.39, 0.40, 0.41),” APL Mater., 2019, doi: 10.1063/1.5097959. [6] T. Samanta et al., “Effects of hydrostatic pressure on magnetostructural transitions and magnetocaloric properties in (MnNiSi)1-x(FeCoGe)x,” J. Appl. Phys., 2015, doi: 10.1063/1.4916339. [7] F. R. Shen et al., “Neutron diffraction study on hydrostatic pressure regulated magnetostructural transition and magnetocaloric effect in MnNi1 - XFexSi1 - yGey alloys,” J. Appl. Phys., 2020, doi: 10.1063/5.0003056. [8] Y. Si et al., “Magnetostructural transformation and magnetocaloric effect of Sn-bonded Mn0.66Fe0.34Ni0.66Fe0.34Si0.66Ge0.34 composite,” Sci. Rep., 2018, doi: 10.1038/s41598-017-18240-x. [9] Z. Y. Wei et al., “Unprecedentedly Wide Curie-Temperature Windows as Phase-Transition Design Platform for Tunable Magneto-Multifunctional Materials,” Adv. Electron. Mater., 2015, doi: 10.1002/aelm.201500076. [10] C. L. Zhang et al., “Tunable magnetostructural coupling and large magnetocaloric effect in Mn1−xNi1−xFe2xSi1−xGax,” J. Magn. Magn. Mater., 2017, doi: 10.1016/j.jmmm.2017.02.046. [11] C. L. Zhang et al., “Magnetostructural transition and magnetocaloric effect in MnNiSi-Fe2Ge system,” Appl. Phys. Lett., 2015, doi: 10.1063/1.4936610. [12] C. L. Zhang et al., “The tunable magnetostructural transition in MnNiSi-FeNiGe system,” Appl. Phys. Lett., 2013, doi: 10.1063/1.4823510. [13] J. Q. Zhao et al., “Tunable magnetostructural phase transition and magnetocaloric effect in Mn1−xNi1−xCo2xSi1−xGexsystem,” J. Alloys Compd., 2017, doi: 10.1016/j.jallcom.2016.12.156. [14] K. Deepak and R. V. Ramanujan, “Magnetocaloric properties of low-cost fe and sn substituted mnnisi-based alloys exhibiting a magnetostructural transition near room temperature,” IEEE Trans. Magn., 2018, doi: 10.1109/TMAG.2018.2832090. [15] K. Deepak and R. V. Ramanujan, “Near room temperature giant magnetocaloric effect in (MnNiSi)1-x(Fe2Ge)x alloys,” J. Alloys Compd., 2018, doi: 10.1016/j.jallcom.2018.02.018. [16] P. Dutta, S. Pramanick, S. Chattopadhyay, D. Das, and S. Chatterjee, “Observation of colossal magnetocaloric effect and its dependence on applied hydrostatic pressure in thermally cycled Mn0.53Fe0.47NiSi0.53Ge0.47 alloy,” J. Alloys Compd., 2018, doi: 10.1016/j.jallcom.2017.11.379. [17] S. Ghosh, A. Ghosh, P. Sen, and K. Mandal, “Giant Room-Temperature Magnetocaloric Effect across the Magnetostructural Transition in (MnNiSi)1-x (FeCoGa)x Alloys,” Phys. Rev. Appl., 2020, doi: 10.1103/PhysRevApplied.14.014016. [18] S. Ghosh, P. Sen, and K. Mandal, “Magnetostructural transition and large magnetocaloric effect in (Mn0.6Fe0.4)NiSi1−xAlx (x = 0.06–0.08) alloys,” J. Magn. Magn. Mater., 2020, doi: 10.1016/j.jmmm.2019.166345. [19] D. Kasimov, J. Liu, Y. Gong, G. Xu, F. Xu, and G. Lu, “Realization of magnetostructural coupling in a high temperature region in Mn0.85Co0.3Ni0.85Si1-xGax system,” J. Alloys Compd., 2018, doi: 10.1016/j.jallcom.2017.10.295. [20] L. Lei et al., “The magnetostructural transition and magnetocaloric properties in Fe0.6Mn0.4NiSi1- xAl xalloys,” J. Appl. Phys., 2020, doi: 10.1063/5.0003261. [21] Y. Li et al., “Windows open for highly tunable magnetostructural phase transitions,” APL Mater., 2016, doi: 10.1063/1.4955214. [22] P. Giannozzi et al., “Advanced capabilities for materials modelling with Quantum ESPRESSO,” J. Phys. Condens. Matter, 2017, doi: 10.1088/1361-648X/aa8f79. [23] P. Giannozzi et al., “Quantum ESPRESSO toward the exascale,” J. Chem. Phys., 2020, doi: 10.1063/5.0005082. [24] P. Giannozzi et al., “QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials,” J. Phys. Condens. Matter, 2009, doi: 10.1088/0953-8984/21/39/395502. [25] R. R Development Core Team, R: A Language and Environment for Statistical Computing. 2011.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5a18e7f6e1ab25eed1a00d6e7a5c447b.jpg)
Figure 1: DFT model performance, phase transition temperature predicted is plotted against the observed experimental data.

![](https://assets.underline.io/uploads/markdown_image/1/image/b9a8448a41632ac63daf60f312ad0c32.jpg)
Figure 2: Workflow of machine learning optimization of MTX alloys.

 Machine Learning Strategies for Screening Mn-T-X (T=Co, Fe, Ni; X=Si, Ge, Sn) Multicaloric Materials

To get more insight into fundamental physical properties and their application relevance, the studies on Rare-earth intermetallic compounds are always remarkable. One of such systems that vastly studied is R2TX3 series (R- Rare-earth element, T- Transition element, and X-p-block element), which shows magnetic properties like spin glass, Kondo interaction, Heavy fermion, skyrmions, etc1,2. Also, the good magnetocaloric properties of the series make them relevant for magnetic cooling applications as well3. In this work, Tb2Ni0.94Si3.2 alloy from the same series has been prepared using the arc melting technique followed by annealing at 1073 K for one week. And magnetic, magnetocaloric, and magnetoresistance properties of the alloy have been investigated. Tb2Ni0.94Si3.2 alloy crystallizes in AlB2-type structure (space group = P6/mmm) with lattice parameters, a = b = 3.9210(3) Å, and c = 4.0044(5) Å, respectively, which are determined from the Rietveld refinement of room temperature powder XRD studies. The magnetic state of the alloy consists of spin-glass behavior around Tf =5.2 K and an antiferromagnetic transition at TN = 12.7 K (See Fig.1). Anomalies corresponding to these magnetic transitions are clearly observed in the variation of DC magnetization with temperature in an applied magnetic field of 0.01 T. Further, the appearance of small thermomagnetic irreversibility at higher temperature ( TN &lt; T &lt; 55 K) denotes the presence of short-range ferromagnetic correlation in the alloy. It is concordant with the positive Curie Weiss temperature (θP = 3.13 K) and slight higher effective magnetic moment of Tb atom (µeff = 9.78 µB/ Tb atom) from the Curie-Weiss fit (@ B=1T). The spin-glass behavior around Tf can be confirmed from the variation of AC magnetic susceptibility with temperature for different frequencies (f =10, 100, and 1000 Hz). As shown in inset of Fig.1.a, the peak corresponding to Tf shows a frequency dependence and shifted to higher temperatures as the AC frequency increases, confirms spin-glass behavior. Along with the reentrant spin glass behavior of the alloy, the magnetic state is marked with successive metamagnetic transitions around BC1 = 1 T and BC2 = 2.5 T in isothermal magnetization data. Studies on magnetocaloric properties of the alloy are done by calculating isothermal entropy change (-ΔSM) and Relative Cooling Power (RCP) from the isothermal magnetization studies. As demonstrated in Fig.2, -ΔSM has reached peak values of 12 J/kg K and 8 J/kg K for a magnetic field change of 9T and 5T, respectively, which is comparable with the other magnetocaloric material in the R2TX3 series like Pr2CuSi3 and Gd2CuSi3 compounds4. Calculated RCP values of the alloy are 504 J/kg and 330 J/kg for ΔB = 9T and 5T, respectively, which are higher than the other compounds5 having the same -ΔSM. Enhanced magnetocaloric effect (MCE) of the alloy is the result of the presence of the short-range correlation, which increases the working temperature span of the material. As an extension to the analysis, the magnetoresistance properties of the alloy were studied. Alloy is noted with a magnetoresistance(MR) of -22% for T = 4 K in B = 9 T. Also, the influence of metamagnetic transition and short-range correlation is reflected in the variation of MR with the applied magnetic field. It denotes the strong correlation between the magnetic and lattice state of the alloy. In conclusion, magnetic, magnetocaloric, and magnetoresistance properties of Tb2Ni0.94Si3.2 alloy shows reentrant spin glass behavior with good MR and enhanced MCE property. Acknowledgment: This research work was supported partially by VEGA 1/0611/18, 1/0705/20 and APVV-16-0079, and project No. 001PU-2-1/2018.

**References:**

1 P. Zhi-Yan, C. Chong-De, B. Xiao-Jun, S. Rui-Bo, Z. Jian-Bang, and D. Li-Bing, Chinese Phys. B 22, 056102 (2012). 2 R. Kumar, K.K. Iyer, P.L. Paulose, and E. V. Sampathkumaran, Phys. Rev. B 101, 144440 (2020). 3 V. Franco, J.S. Blázquez, J.J. Ipus, J.Y. Law, L.M. Moreno-Ramírez, and A. Conde, Prog. Mater. Sci. 93, 112 (2018). 4 F. Wang, F. Yuan, J. Wang, T. Feng, and G. Hu, J. Alloys Compd. 592, 63 (2014). 5 L. Li, D. Huo, Z. Qian, and K. Nishimura, J. Phys. Conf. Ser. 263, 2 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/81a75c94ad45a9b5801f82776076af93.jpg)
Fig.1.Variation of DC magnetic susceptibility (M/B) as a function of temperature in applied magnetic field B = 0.01 T. Inset shows AC magnetic susceptibility for frequencies 10,100 and 1000 Hz.

![](https://assets.underline.io/uploads/markdown_image/1/image/1e209a16d7d503cbccef602dcd3d78f3.jpg)
Fig.2. Variation of isothermal entropy as a function of temperature

 Influence of Short-Ranged Correlation on Magnetocaloric Properties of Tb2Ni0.94Si3.2 Alloy

1. Entropy change of successive martensitic transformations in Ni-Mn-Ga Heusler alloys can be utilized to realize enhanced magnetocaloric properties. A detailed study of phase transformations of Ni2.15Mn0.85Ga, (ΔQ = 4900 J/kg at 343 K and 140 kOe) is reported here. Upon cooling, paramagnetic austenite (L21) transforms into a ferromagnetic 7M monoclinic martensitic phase. This phase is stable in a narrow temperature range and, upon further cooling, transforms into a non-modulated ferromagnetic tetragonal (L10) phase. The separation between the equilibrium temperatures of the L21 and the L10 phases is only ~50 K. The alloy undergoes reversible temperature-induced martensitic and inter-martensitic phase transformations with thermal hysteresis about 25 K. The conclusions from the detailed study of the phase transformations lead to new possibilities to enhance the magnetocaloric effect by utilizing the entropy associated with multi-structural transformations. 2. Introduction Magnetic cooling based on the giant magnetocaloric effect (GMCE) is a proposed solution to the low-efficiency and eco-adverse refrigerant of current technologies [1]. Developing a material that produces a GMCE near room temperature is key to the more efficient and economical cooling technology. Ni-Mn-X alloys are under the spotlight because they are inexpensive and non-toxic. The isothermal entropy changes exhibited by some Ni-Mn-Ga alloys are in close range or even higher than those reported in Gd and La-based compounds [2]. Several techniques are available to enhance the GMCE demonstrated by Ni-Mn-X alloys. Combining magnetocaloric and elastocaloric effects by applying stress to the refrigerants is one technique [3]. The latest trend is to utilize the two consecutive structural transformations of these alloys [4]. Here we report a study of the inter-martensitic phase transformations of such an alloy. The analysis of the structures, phase transformation temperatures, and the thermal hysteresis will support the search for new avenues to enhance the magnetocaloric effect by utilizing the entropy associated with multi-structural transformations [5]. 3. Experimental A polycrystalline sample was prepared by arc-melting in an argon atmosphere and then annealed at 1073 K for 50 hours [6]. The chemical composition, Ni2.15Mn0.85Ga, was determined by energy dispersive spectroscopy. In-situ synchrotron diffraction data were collected at beamline 11-ID-C of the Advanced Photon Source at Argonne National Laboratory (λ = 0.010804 nm). Diffraction data were analyzed using the General Structure Analysis System EXPGUI [7]. Magnetization measurements were done using a SQUID magnetometer. 4. Results and Discussion The diffraction data (Fig. 1) at selected temperatures (400-100 K) shows that the alloy undergoes martensitic and inter-martensitic transformations and mixtures of phases in different temperature intervals. The austenitic structure is cubic L21 (Fm-3m space group). Upon cooling, the alloy transforms into a 7M monoclinic (P 1 2/m 1 space group). Upon further cooling, it transforms into a non-modulated tetragonal L10 structure (I 4/m m m space group). The thermograms (Fig. 2) were constructed by the calculated phase fractions obtained from Rietveld refinements. The alloy undergoes martensitic transformation around 310 K from austenite to 7M modulated martensite. Upon further cooling (~ 260 K), the inter-martensitic phase transformation [8] occurs from monoclinic to tetragonal phase. The reverse-phase transformations occur while heating (see fig. 2). The characteristic temperatures of the austenitic (TMH), martensitic (TMC), and inter-martensitic transformations (TIMH and TIMC) were defined at 50% phase fraction of the respective phases upon cooling and then heating, respectively. Thermal hystereses of the transformations, calculated by the differences between TMH & TMC and between TIMH & TIMC, respectively, are very close (~25 K). Because of the similar hysteresis, the separation between the martensitic and inter-martensitic transformation temperatures, while heating and cooling, are the same and is ~50 K. The austenitic phase is paramagnetic, and the martensitic phases are ferromagnetic. The austenitic phase transformation temperature (332 K) and Curie temperature (337 K) are very close. Under a suitable field, these two transformations could coincide to give a much higher MCE. 5. Conclusions and Future work The alloy undergoes two successive phase transformations with narrow separation between them (~50 K). The hystereses are less than 25 K. These conditions suggest that utilizing two successive phase transformations may result in higher GMCE. To optimize the GMCE, extensive knowledge of two transformations is required. The magnetic phase transformation temperature increases with increasing magnetic field [6]. However, the behavior of the crystalline phase transformation temperatures under magnetic fields is unknown and essential to study. Also, isothermal magnetization measurements could reveal the possible magnetic phase transformations.

**References:**

1. D. R. Brown, N. Fernandez, J. A. Dirks, U.S. Department of Energy, (2010) 2. J. Liu, T. Gottschall, K. P. Skokov, nature materials, Vol. 11.7, p.620-626 (2012) 3. Y. Hu1, Z. Li, B. Yang, APL Materials Vol.5, p.046103 (2017) 4. Z. Li, K. Xu, Y. Zhang, Scientific Reports, Vol. 5, p.15143 (2015) 5. Z. Li, Y. Zhang, C. F. Sanchez-Valdes, Appl. Phys. Lett., Vol.104, p.044101 (2014) 6. A. Kamantsev, V. Koledov, A. Mashirov, J. Appl. Phys., Vol. 117, p.163903 (2015) 7. B. H. Toby, J. Appl. Cryst., Vol. 34, p.210-213 (2001) 8. S.M. Konoplyuk, V.V. Kokorin, Ukr. Phys. J. Vol.43, p.1275 (1998)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f4d4617604cc887d5b8421a9c3cb488f.jpg)
Diffraction patterns collected while cooling from 395 to 100 K. At 395 K, the alloy is austenitic, and upon cooling, it transforms into a 7M monoclinic phase. Upon further cooling, it transforms into a tetragonal L10 structure.

![](https://assets.underline.io/uploads/markdown_image/1/image/952feea6b45327a2d71ceb6d345b754d.jpg)
Variation of the three phases' phase fractions upon heating (red) and cooling (blue). Characteristic temperatures of the martensitic and inter-martensitic phase transformations were determined by the intersections as shown.

 Temperature-induced successive martensitic and inter-martensitic phase transformations of Ni2.15Mn0.85Ga Heusler alloy

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

Power law to express the field dependence of the isothermal entropy change (ΔsT ∝ ΔHn) has been widely employed for obtaining information of the thermomagnetic second-order phase transitions (e.g. critical exponents [1] or Curie temperatures [2]). Recently, the analysis of this field dependence has been extended to materials undergoing thermomagnetic first-order phase transitions, the most promising magnetocaloric materials up to the moment. It has been shown that the value of the exponent n overshoots above 2 for first-order phase transitions, while it does not overshoot for the second-order case, allowing to establish a quantitative criterion for determining the order of the phase transitions [3]. This is in excellent agreement with previous phenomenological observations, supporting the validity of the proposed criterion. For direct magnetocaloric effect (MCE), the overshoot feature for fingerprinting first-order transitions can be validated in the frame of the Bean-Rodbell model [4], obtaining an excellent agreement between experiments (e.g., for La(Fe,Si)13 which undergoes a ferromagnetic (FM) to paramagnetic (PM) magnetoelastic transition [5]) and the model. However, for inverse MCE, the validity of the proposed criterion and the characteristics of the field dependence have only been studied experimentally. In this work, the magnetic field dependence of the inverse MCE is analyzed using a mean field approach for describing antiferromagnetic (AF) to FM magnetoelastic transitions. The model is able to describe both second- and first-order phase transitions through the introduction of a magnetovolume energy term according to the Callen-Callen theory [6] (having a Gibbs energy term of the form -βωM2/4 , being ω the relative volume change, M the magnetization and β an introduced magnetoelastic coupling parameter). Using this model, we are able to reproduce the experimentally observed features for the exponent n, showing the existence of the characteristic overshoot for first-order transitions (which corresponds to β&gt;0) and its absence for second-order ones (β=0), as shown in Fig. 1. We explore the influence of different parameters of the model on exponent n, such as the transition temperature and Curie temperature separation or the exchange constant between the moments of the different sublattices. The existence of the overshoot feature is corroborated for all the different cases. This supports the extension of the quantitative criterion to AF-FM phase transitions and set the basis for the analysis of exponent n in these materials. A main difference with respect to direct MCE is that negative values of the exponent n are obtained at temperatures close to the transition. This is ascribed to the reduction of the inverse MC response due to the influence of the unavoidable FM to PM transition at higher temperatures. The obtained features for exponent n (field dependence and temperature dependence) are qualitatively compared to those of GdBaCo2O6 [7] (AF to FM magnetoelastic transition), showing a good agreement between both the experiment and the model. The obtained results are extrapolated to understand the behavior of the exponent n for a Ni49Mn36In15 sample [8] (low magnetization to high magnetization magnetostructural transition). 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 and Sevilla University under VI PPIT-US program.

**References:**

[1] V. Franco, A. Conde, Int. J. Refrig. Vol. 33 pp. 465–473 (2010) [2] L.M. Moreno-Ramírez, J.S. Blázquez, V. Franco et al., IEEE Magn. Lett. Vol. 7 Art no. 6102004 (2016) [3] J.Y. Law, V. Franco, L.M. Moreno-Ramírez et al., Nat. Commun. Vol. 9 Art no. 2680 (2018) [4] C.P. Bean, D.S. Rodbell, Phys. Rev. Vol. 126 pp. 104–115 (1962) [5] L.M. Moreno-Ramírez, C. Romero-Muñiz, J.Y. Law et al., Acta Mater. Vol. 175 pp. 406–414 (2019) [6] E. Callen, H.B. Callen, Phys. Rev. Vol. 139 p. A455–A471 (1965) [7] J.Y. Law, V. Franco, A. Conde et al., J. Alloys Compd. Vol. 777 pp. 1080–1086 (2019) [8] J.Y. Law, Á. Díaz-García, L.M. Moreno-Ramírez et al., Acta Mater. Vol. 166 pp. 459–465 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3c9078ab03a39d089b10c5aa280ea645.jpg)
Fig. 1. Temperature dependence of exponent n for different magnetovolume coupling parameter β. Inset: maximum value of the overshoot above 2 as a function of β.

 Analysis of the Magnetic Field Dependence of the Isothermal Entropy Change of Inverse Magnetocaloric Materials

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.

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