France



Power law to express the field dependence of the isothermal entropy change (Δ&lt;i&gt;s&lt;sub&gt;T&lt;/sub&gt;&lt;/i&gt; ∝ Δ&lt;i&gt;H&lt;sup&gt;n&lt;/sup&gt;&lt;/i&gt;) 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 &lt;i&gt;n&lt;/i&gt; 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)&lt;sub&gt;13&lt;/sub&gt; 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 -βω&lt;i&gt;M&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;/4 , being ω the relative volume change, &lt;i&gt;M&lt;/i&gt; the magnetization and β an introduced magnetoelastic coupling parameter). Using this model, we are able to reproduce the experimentally observed features for the exponent &lt;i&gt;n&lt;/i&gt;, showing the existence of the characteristic overshoot for first-order transitions (which corresponds to β&amp;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 &lt;i&gt;n&lt;/i&gt;, 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 &lt;i&gt;n&lt;/i&gt; in these materials. A main difference with respect to direct MCE is that negative values of the exponent &lt;i&gt;n&lt;/i&gt; 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 &lt;i&gt;n&lt;/i&gt; (field dependence and temperature dependence) are qualitatively compared to those of GdBaCo&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;6&lt;/sub&gt; [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 &lt;i&gt;n&lt;/i&gt; for a Ni&lt;sub&gt;49&lt;/sub&gt;Mn&lt;sub&gt;36&lt;/sub&gt;In&lt;sub&gt;15 &lt;/sub&gt;sample [8] (low magnetization to high magnetization magnetostructural transition).&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), 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)&lt;br/&gt;[2] L.M. Moreno-Ramírez, J.S. Blázquez, V. Franco et al., IEEE Magn. Lett. Vol. 7 Art no. 6102004 (2016)&lt;br/&gt;[3] J.Y. Law, V. Franco, L.M. Moreno-Ramírez et al., Nat. Commun. Vol. 9 Art no. 2680 (2018)&lt;br/&gt;[4] C.P. Bean, D.S. Rodbell, Phys. Rev. Vol. 126 pp. 104–115 (1962)&lt;br/&gt;[5] L.M. Moreno-Ramírez, C. Romero-Muñiz, J.Y. Law et al., Acta Mater. Vol. 175 pp. 406–414 (2019)&lt;br/&gt;[6] E. Callen, H.B. Callen, Phys. Rev. Vol. 139 p. A455–A471 (1965)&lt;br/&gt;[7] J.Y. Law, V. Franco, A. Conde et al., J. Alloys Compd. Vol. 777 pp. 1080–1086 (2019)&lt;br/&gt;[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 &lt;i&gt;n &lt;/i&gt;for different magnetovolume coupling parameter β. Inset: maximum value of the overshoot above 2 as a function of β.



INTERMAG 2021

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

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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.

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.

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L10-ordered MnAl shows a high magnetic moment of 2.4 μB/f.u. and magnetocrystalline anisotropy constant (K) of 1.5 MJ/m3 [1,2]. The magnetocrystalline anisotropy and spin direction can be tuned by either the axial ratio c/a or substituting the Mn of MnAl by transition metals. Sakuma calculated Ku of L10-ordered equiatomic MnAl as a function of the axial ratio c/a ranging from 0.60 to 1.2 by first-principles calculation [1]. It was found that the spin direction changes to the out-of-plane direction (uniaxial) from the in-plane direction at c/a = 0.7071 by changing the magnetocrystalline anisotropy sign to positive from negative. The calculated magnetocrystalline anisotropy constant is 1.5 MJ/m3 at c/a = 0.9058. Sakuma used the lattice constants of a =3.93 Å and c =3.56 Å measured at 300 K in his first-principles calculations. On the other hand, Manchanda et al. have performed the first-principles calculation on Fe-substituted L10-ordered MnAl to investigate magnetocrystalline anisotropy constant and found that Fe increases the magnetocrystalline anisotropy constant to 2.5 MJ/m3 from 1.5 MJ/m3 of non-substituted MnAl. However, the total magnetic moment decreased, and the spin direction did not change [3]. Neither Sakuma nor Manchanda reported the Curie temperature for various c/a MnAl and Fe-substituted MnAl and relaxed the studied MnAl system. In this paper, we have systematically investigated the effects of transition metals (Fe, Co, Ni) on magnetization, magnetocrystalline anisotropy, and Curie temperature of L10-ordered MnAl. We used the WIEN2k package based on density functional theory (DFT) and the full-potential linearized augmented plane wave (FPLAPW) method to conduct the first-principles calculations [4]. All calculations used 19 × 19 × 27 k-point mesh generating 1400 k-points in the irreducible part of the Brillouin zone to obtain electronic structures of Mn0.5TM0.5Al (TM = Mn, Fe, Co, and Ni). Each TM has the following valence electrons (n): 7 for Mn (3d5 4s2), 8 for Fe (3d6 4s2), 9 for Co (3d7 4s2), and 10 for Ni (3d8 4s2). After having relaxed L10-ordered Mn0.5TM0.5Al (TM = Mn, Fe, Co, and Ni), we obtained the lattice constants, volumes, and c/a ratios in Table 1. It is found that the c/a ratio and volume decrease with an increase in n from 7 (Mn) to 10 (Ni) in Table 1. Figure 1 shows the density of states (DOS) for Mn0.5TM0.5Al (TM = Mn, Fe, Co, and Ni) with spin configuration. DOS significantly changes with the TM substitution. It is striking that Ni-substituted MnAl shows the ferrimagnetic spin configuration, as seen in Fig. 1(d). However, the ferromagnetic spin configuration is set in Mn0.5TM0.5Al (TM = Mn, Fe, and Co). As summarized in Table 1, the total magnetic moment decreases as the valence electron increases in the order of Ni, Co, and Fe. In order to calculate the K of the Mn0.5TM0.5Al system, the magnetocrystalline anisotropy energy (MAE) was calculated using the total energy difference between &lt;001&gt; and &lt;100&gt; spin configurations (ΔE = E&lt;001&gt; - E&lt;100&gt;). The Fe substitution leads to a significant increase in K from 1.34 MJ/m3 to 2.98 MJ/m3. When either Co or Ni replaces Fe, the K becomes negative and is -0.3 MJ/m3 for Co or -0.18 MJ/m3 for Ni in Table 1. This implies the magnetization (Co, Ni) direction changes to the in-plane direction from the out-of-plane direction, i.e., uniaxial (Mn and Fe). Curie temperature (TC) was calculated by the mean-field approximation (MFA). The TC dramatically decreases from 685 K(Mn) to 20 K(Ni). Alloying the MnBi with transition elements could tune the spin direction and magnetocrystalline anisotropy of L10-ordered MnAl. However, magnetization and Curie temperature are negatively affected by the alloying. We will discuss all these findings in detail in this presentation. * This work was supported in part by the E. A. “Larry” Drummond Endowment at the University of Alabama.

**References:**

[1] A. Sakuma, J. Phys. Soc. Jpn. 63, 1422 (1994) [2] J. H. Park, Y. K. Hong, et al., J. Appl. Phys. 107, 09A731 (2010) [3] P. Manchanda, et al., J. Magn. Magn. Mater, 365, 88-92 (2014) [4] Blaha, P. and Schwarz, K., WIEN2k: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz Techn. Universität Wien, Vienna, Austria, 2001)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/aecee2e75cceaee3a872a555081225de.jpg)
Table 1. Lattice parameters and magnetic properties of L10-Mn0.5TM0.5Al (TM = Mn, Fe, Co, Ni).

![](https://assets.underline.io/uploads/markdown_image/1/image/8c515420a3e4c27b6c54c6fa18f1b9d9.jpg)
Figure 1. Density of states (DOS) for (a) MnAl, (b) Mn0.5Fe0.5Al, (c) Mn0.5Co0.5Al, and (d) Mn0.5Ni0.5Al based relaxed lattice constants.

 Tuning Spin and Magnetocrystalline Anisotropy of L10-ordered MnAl with Transition Metal Elements (TM = Mn, Fe, Co, Ni)*

Nowadays the use of permanent magnets (PMs) plays a key role in different applications such as energy and electromobility. In order to obtain a high magnetic performance, the most extended choice is PMs containing rare-earths (REs). Alternative RE-free PM materials are investigated to plug the gap between ferrites and NdFeB magnets [1]. MnAlC alloy is a promising RE-free PM candidate, but further optimization is required in order to achieve a proper combination of saturation magnetization (provided by the only ferromagnetic phase of the system: L10 or τ-MnAl) and coercivity. Studies on MnAl alloys typically focus on obtaining a maximum content of τ-phase, which results in an optimized saturation magnetization [2]. We have recently shown the possibility of developing coercivity in gas-atomized MnAl powder by applying milling times as short as 30-270 s via the self-developed “flash milling” method [3]. A successful combination of nanostructuring and a controlled phase transformation process is behind the observed increase in coercivity [3]. In this study we have used ε-phase MnAlC powder produced by gas-atomization and flash-milling (60 s) to fabricate MnAlC bulk magnets, with no need to transform previously the ε into τ phase. Under the optimal combination of pressure (300 MPa) and temperature (600 °C), hot-pressing applied to ε-phase MnAlC alloy has been able to manage simultaneously the ε-to-τ transformation and the powder compaction to end with a high-density (93%) MnAlC magnet [4]. Figure 1(a) shows the X-ray diffraction pattern of the precursor ε-phase loose powder and the successful transformation into τ-phase after the hot-pressing process. The room temperature hysteresis loops measured for the hot-pressed magnet showed an enhancement of the coercivity of up to 25 % and a slightly superior magnetization at remanence by comparison with the annealed gas-atomized loose powder (Fig. 1 (b)). The large coercivity obtained for the magnet may be explained based on the formation of both β-Mn and Mn3AlC phases together with a reduced mean crystallite size (27 nm) and the induced strain during compaction [4]. On this basis, we have demonstrated that coercivity of the compacted magnet can be further increased in about 15% by starting from flash-milled gas-atomized powder, due to a larger content of β-Mn and Mn3AlC phases. We have obtained comparable magnetization and coercivity values when compacting the starting material with a crystallographic structure based on τ-phase (i.e., involving two steps: annealing for managing ε into τ phase transformation followed by hot-pressing), thus validating our single-step process. This is a promising cost-efficient route which opens the path to new possibilities for the fabrication of MnAlC-based magnets. Acknowledgements IMDEA acknowledges financial support from EU M-ERA.NET and MINECO through the projects "NEXMAG" (Project Success Case at H2020 M-era.Net Programme, 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 collaboration "ECNanoManga".

**References:**

[1] J.M.D. Coey, IEEE Trans. Magn., 47, 4671 (2011) [2] V. Øygarden et al., J. Alloys Compd., 779, 776 (2019) [3] J. Rial et al., Acta Mater., 157, 42 (2018); Engineering, 6 (2), 173 (2020) [4] C. Muñoz-Rodríguez et al., J. Alloys Compd., 847, 156361 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ee90b2b1fd40d0e1617728e809b5f480.jpg)
Fig. 1. (a) X-ray diffraction pattern of the ε-phase gas-atomized loose powder and hot-pressed powder. (b) Room temperature hysteresis loops (second quadrant) of the loose annealed powder (ε transformed into τ-phase) and the magnet obtained by hot-pressing the ε-phase powder. Inset shows an image of the resulting compacted MnAlC magnet.

 MnAlC Permanent Magnets Obtained Directly from ε-Phase Gas-Atomized and Milled Powder by Hot-Pressing

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

In recent years, magnetic nanocomposites (NCs) have obtained an ever-increasing attention, due to the possibility to finely control and modify their features at the nanoscale, which is fundamental for extending their applicability as permanent magnets in a multitude of energy-related technological areas [1,2]. In this regard, ferrites have shown to be a promising class of materials, in particular M-type SrFe12O19 (SFO) and spinel CoFe2O4 (CFO) nanoparticles (NPs): their respective hard and soft magnetic properties make them interesting candidates for hard-soft exchange-coupled nanostructures. Effectively, the combination of two prototypical phases with different extrinsic properties expands the potentiality and hence the suitability of such nanosystems [3]. Our main focus here is on the investigation of the synthesis strategy in controlling the magnetic coupling, through the optimization of the interface between the hard-soft magnetic phases, thus achieving efficiently strongly coupled nanostructures. This work addresses a systematic investigation of the magnetic interaction in SFO-CFO hard-soft NCs. Several samples were synthesized through a self-combustion sol-gel approach, with compositions ranging from 50/50 to 90/10 w/w %, in step of 10%. In order to elucidate the synthesis method, a thermogravimetric/differential thermal analysis (TG/DTA) was performed, showing a first evidence that the reaction proceeds in a symbiotic way, where the formation of CFO after-combustion assists the evolution of SFO precursors, when the CFO % is increased [4]. The subsequent investigation on the inner structure of the NCs, by transmission electron microscopy (TEM) technique, revealed that SFO NPs are in the form of platelets, with CFO nanocrystals confined between the SFO ones. This clearly suggests a strong interaction between the two structures [5]. The evidence of a symbiotic growth was furtherly confirmed by X-ray powder diffraction (XRPD): the crystallite size extracted by Rietveld refinement shows an evident dependence of SFO crystallite size on the amount of inserted soft phase. When CFO increases, the dc (size extracted along the c-axis) and dab (size extracted along the ab-plane) for SFO drop from 104 to 51 nm from 132 to 77 nm, respectively. Hence, we illustrate here for the first time that the CFO grains act as nucleation sites for the SFO phase, resulting in an effect of confinement, which restricts the growth of one phase by the other. To clarify the relationship between the morphological-structural features and magnetic coupling, the static magnetic properties of NCs were investigated at 300 K using a superconducting quantum interference device (SQUID) magnetometer. The analysis of field-dependent magnetization loops shows that the two magnetic phases are homogeneously dispersed and strongly coupled (as reported in Figure 1). Furthermore, the switching field distributions clearly exhibit a single reversal process of magnetization, confirming that the SFO and CFO phases are strongly coupled in the composite (as shown in Figure 2). As expected, the variation of coercivity (HC) is consistent with the increasing amount of soft CFO phase, as it decreases from ~463 to 178 kA/m, within the limit of exchange-coupling, whereas the saturation moment (MS) increases up to ~74 Am2/kg. Our study shows that it is possible to control and limit the decrease of the coercivity of hard-soft bi-magnetic NCs to our desire by controlling the size and distribution of the hard-soft regions, and their interface. We thank the Swedish Energy Agency and Swedish Research Council (VR) for financially supporting this work.

**References:**

[1] R. Skomski, P. Manchanda, P. K. Kumar, B. Balamurugan, A. Kashyap, D. J. Sellmyer, IEEE Trans. Magn. , 49 (7), 3215, (2013) [2] K. P. Skokov, O. Gutfleisch, Scr. Mater., 154, 289, (2018) [3] G. Muscas, P. Anil Kumar, G. Barucca, G. Concas, G. Varvaro, R. Mathieu, D. Peddis, Nanoscale, 8, 2081, (2016) [4] F. Sayed, G. Kotnana, G. Muscas, F. Locardi, A. Comite, G. Varvaro, D. Peddis, G. Barucca, R. Mathieu, T. Sarkar, Nanoscale Adv., 2 (2), 851, (2020) [5] P. Maltoni, T. Sarkar, G. Varvaro, G. Barucca, S. Ivanov, D. Peddis, R. Mathieu, J. Phys. D: Appl. Phys., in print, (2020), doi:10.1088/1361-6463/abd20d,

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/216005caea78a23890b0a81308d7264d.jpg)
Fig.1 Magnetization M vs. magnetic field H curves for SFO, SFO-CFO 50/50 w/w % and CFO at 300K

![](https://assets.underline.io/uploads/markdown_image/1/image/9b44e3133f0dd8474dbde85d43ae2b6b.jpg)
Fig.2 Normalized irreversible susceptibility χirr vs reverse magnetic field H for SFO, SFO-CFO 50/50 w/w % and CFO at 300K; the inset shows the MDCD vs H.

 Morphology, structure and magnetic coupling relationship in hard-soft SrFe12O19-CoFe2O4 nanostructures

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.

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

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

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