High-entropy alloys (HEAs), instead of employing one or two main constituents like in traditional alloy development, adopt a different design concept where it combines a blend of multi-principal elements in large concentrations. This design idea enables them with large values of configurational entropy of mixing and a vast compositional space which offers a huge window of exploration opportunities. Magnetocaloric HEAs have been limited to low-temperature range or showing sub-par performance till recent extensions to the first-generation equiatomic HEA design approach have been devised [1, 2]. The magnetocaloric performance of equiatomic magnetocaloric HEAs heavily depends on the choice of element selection and thus the likelihood of relying on the rare-earth (RE) elements due to their intrinsic large magnetic moments. Extending beyond the equiatomic point towards non-equiatomic in the HEA region combined with directed search strategies, overcomes the above-mentioned limitations of magnetocaloric HEAs: the low temperature limit is improved (48 % increase as displayed in Fig 1) and â‰¥ 5-fold performance enhancement (Fig 2) [3-5]. In this talk, we will show the various design strategies of magnetocaloric HEAs and how to tackle the vast HEA space to tune for the desired magnetocaloric properties. Work supported by Grant PID2019-105720RB-I00 funded by MCIN/AEI/ 10.13039/501100011033. Additional support ConsejerÃ­a de EconomÃ­a, Conocimiento, Empresas y Universidad de la Junta de AndalucÃ­a (grant P18-RT-746), US Air Force Office of Scientific Research (FA8655-21-1-7044) and Sevilla University under VI PPIT-US program.

Tuning in the vast high entropy alloy space for competitive magnetocaloric properties

Exceptional tunability in the electronic and magnetic properties makes Heusler compounds very promising from both the fundamental and applied perspectives. Half-metallic ferromagnetism, half-metallic fully-compensated ferrimagnetism, spin-gapless semiconducting behavior, and fully-compensated ferrimagnetic spin-gapless semiconducting behavior have been predicted or demonstrated experimentally in Heusler compounds which makes them suitable for applications in a number of novel spintronic devices1,2,3,4,5. Half-metallic Co-based Heusler alloys are among the most attractive systems due to their high Curie temperatures, high spin polarization and the structural similarity to binary semiconductors6,7,8. Spin-gapless semiconductors can be regarded as a combination of gapless semiconductors and half-metallic ferromagnets where the conducting electrons or holes are not only 100% spin polarized but also easily excited. The realization of spin-gapless semiconducting behavior in Heusler alloys is expected to fulfill the needs for semiconductor spintronics. In this work, we have introduced the substitution of low valence transition metal atoms Y = Ti, V, Cr, Mn, and Fe to Co atoms in the parent Co2FeGa system, and examined the properties of quaternary Heusler compounds Co2-xYxFeGa (x = 0.50), both experimentally and theoretically to get a global overview of the electronic, magnetic, electron transport and mechanical properties. All single-phase alloys exhibit Heusler like L21 ordering, as corroborated by X-ray diffraction. The low-temperature saturation magnetic moments agree fairly well with the values expected from a Slater-Pauling rule for half metals (Fig.1). Electrical transport measurements are performed to explain the electronic structure of the alloys. The temperature dependence of electrical resistivity for Mn substituted alloy shows semiconducting nature in the complete temperature regime (5-400)K (Fig.2). Ab initio calculations are also performed to understand the experimental findings.

![](https://assets.underline.io/uploads/markdown_image/1/image/14f7b59db99b038cf74a4718f8f85273.jpg)

The variation of saturation magnetic moment with valence electron counts per formula units with element Y.

![](https://assets.underline.io/uploads/markdown_image/1/image/4d76d8c1a433798c5183033756315811.jpg)

Temperature dependence of electrical resistivity in Co1.50Mn0.50FeGa at zero magnetic field showing semiconducting behavior.

Possible half-metallic and spin-gapless semiconducting behavior in quaternary Heusler compounds Co2-xYxFeGa (Y = Ti, V, Cr, Mn, Fe, and Co, x = 0.50)

Additive manufacturing (AM) is becoming an alternative to traditional manufacturing methods [1]. In the most extended AM method (fused deposition modeling, FDM), a polymeric filament is extruded above its melting point for its deposition into thin layers. There is a high interest in the use of composite filaments, formed by a polymeric matrix with functional fillers, for the AM of functional parts [2]. The quality of the FDM printed parts is highly dependent on the uniformity of the filament diameter. In the case of composite filaments, a homogeneous distribution of the fillers is also crucial to have a reproducible and uniform functionality. Homogeneous soft magnetic PLA composite filaments for FDM have been recently reported, in which a customized feedstock of polymeric capsules filled with the functional fillers is employed [3]. Fig. 1 shows that composite filaments exhibit a soft magnetic behavior. Additionally, they all have a demagnetizing factor of ~ 1/3 (spheres, according to the shape of the gas atomized powders) regardless of the concentrations of fillers (up to 52 wt. %, corresponding to 12 vol. %). The addition of the fillers causes a remarkable shift in the thermal degradation temperature of the polymer. Increasing filler content produces an abrupt drop in the complex modulus of the polymer above its glass transition, which shifts to lower temperatures according to the peak of tan(δ) (Fig. 2). A decrease in the viscosity in liquid state is also observed, which causes a reduction of the extrudability and printability of the filaments for filler contents above 30 wt. %. The reduction of the viscosity of the composites requires the lowering of the temperatures for their extrusion and printing with respect to the typical ones for PLA. 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.

![](https://assets.underline.io/uploads/markdown_image/1/image/87db25ab60c9820e49c23306bd80571d.jpg)

Fig. 1. Magnetization vs. magnetic field for the raw maraging steel powder and composite filaments.

![](https://assets.underline.io/uploads/markdown_image/1/image/245b4256f10c5e8a2ffe7ab44cd407d4.jpg)

Fig. 2. (a) Complex modulus and (b) tan(δ) of raw PLA and composite filaments.

Manufacturing and Characterization of Soft Magnetic Composite Filaments for Additive Manufacturing

High-entropy alloys (HEAs), based on the design concept of mixing five or more principal elements to yield high entropy of mixing (ΔSmix), expands the compositional space of multicomponent materials when compared to conventional materials, which are mainly based on one or two main constituents. HEAs, thus, form compositions without dominant elements, in which new materials with excellent properties, some of them being superior or unique compared to the conventional materials, have been found [1]. These advantages prompted a large surge in studying HEAs, with the explored compositions evolving from first-generation single phase equiatomic to second-generation multiphase non-equiatomic HEAs. The latter are recently reported with properties that outdo those of the first-generation HEAs, such as excellent strength-ductility combination, surpassing the low temperature limit, or enhanced magnetocaloric properties of rare-earth-free high-entropy alloys owing to a first-order magnetic phase transition [1-3]. Here, we present, when tuning CoCrMnNiTi alloys from conventional to the high-entropy region (i.e. ΔSmix &gt; 1.5 R, where R is the gas contstant, 8.314 J mol-1 K-1), the evolution of their thermomagnetic and magnetocaloric behavior. The obtained HEA has a martensitic temperature tuned nearer to room temperature and a 10% increase in the entropy change (Fig. 1). This work demonstrates the recently proposed claim [1-3] that it is possible to obtain high-performance magnetocaloric materials within the HEA compositional space. 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.

![](https://assets.underline.io/uploads/markdown_image/1/image/ac398a967db02e43d38fa8ceed0d87a5.jpg)

Fig 1. The variation of martensitic transition temperatures (square symbols) and entropy change at the transition (circular symbols) after tuning a conventional alloy towards the high-entropy region (ΔSmix > 1.5 R).

Tuning conventional alloys towards the high-entropy space: thermomagnetic and magnetocaloric behavior

The use of composites combining a thermoplastic and functional fillers for additive manufacturing (AM), as in fused deposition modeling, FDM, provides a path for low cost development of functional parts with complicated geometries [1]. Magnetic refrigeration requires refrigeration beds with intricate geometries for the passage of the heat transfer fluid. Heusler alloys exhibiting magneto-structural transformation (MST) are attracting enormous attention as they can show a large response without relying on critical elements [2]. However, machinability of these alloys is compromised, making AM attractive for the fabrication of the refrigerator beds. Off-stoichiometry Ni2MnGa Heusler powder has been obtained by ultrasonic atomization, resulting in spheric particles subsequently sieved at 100 μm (Fig. 1). Differential scanning calorimetry (DSC) enabled to identify the MST in the atomized Heusler alloy (Fig. 2(a)). This powder was used to fill customized PLA capsules that were used as the feedstock for the extrusion of composite filaments for FDM according to the method showed in Ref. [3]. Composite filaments were manufactured with different concentrations of fillers ranging from 30 to 64 wt. %, determined by thermogravimetric analysis, TGA, (Fig. 2(b)). As the particles were not subjected to high temperatures during the extrusion of the filaments (less than 200 °C) , the phases present in the alloy do not change. The AM of magnetocaloric parts can avoid the shape limitation and, in this case, the polymer matrix would prevent the weakening of the structure due to the successive volume changes taking place with the cyclical occurrence of an MST. 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 POB “Technologie Materialowe” of Warsaw University of Technology within the Excellence Initiative: Research University (IDUB) program.

![](https://assets.underline.io/uploads/markdown_image/1/image/4e2d2b38f53f80505a1d801ab989ac98.jpg)

Fig. 1. Scanning electron micrograph of Ni2MnGa powder.

![](https://assets.underline.io/uploads/markdown_image/1/image/50cf44b9c97b07a7d8704c2818ad4355.jpg)

Fig. 2. (a) DSC results of Heusler powder and (b) TGA curves of raw PLA and PLA-based composite filaments.

Magnetocaloric Heusler Alloy Composites for Fused Deposition Modeling

High-entropy alloys (HEAs), whose new alloy design concept with multiple principal elements, attracted a lot of attention for structural application and functional aspects. Since their first report in 2004, their compositions have developed from first generation with quinary equiatomic single-phase to second-generation multi-phase structure with non-equiatomic compositions. For magnetocaloric HEAs, their limitations have been recently found to be overcome by using non-equiatomic HEA compositions: GdTbCoAlFe (with Curie temperatures up to 108 K) overcomes the low temperature limit of the rare-earth-containing HEAs (typically saturates around &lt; 60 K) [1,2] and the first-order magnetostructural phase transition in FeMnNiGeSi surpasses the smeared out magnetocaloric effect (MCE) of rare-earth-free HEAs [3,4]. In this work, we further enhance the MCE of non-equiatomic Gd34.9Tb19.4Co19Al23.3Fe3 HEA through microstructural control, in which the alloy microwires are annealed using the current density annealing technique. Induced nanocrystals in the amorphous matrix observed from transmission electron microscopy (TEM) are found to increase and grow with the current density magnitude (Fig. 1). This leads to an increase in the working temperature span of the HEA microwires and at the same time offers a relative cooling power (RCP) comparable to many reported amorphous MCE alloys, both conventional alloys and HEAs (Fig. 2). Our findings pave a pathway for further optimizing MCE through appropriate processing methods on top of careful alloy design selection.

![](https://assets.underline.io/uploads/markdown_image/1/image/fce97f9433fab8f05b035a2bf2ea02e2.jpg)

Fig. 1 TEM results of the (a) as-cast and annealed Gd34.9Tb19.4Co19Al23.3Fe3 microwires using current density values of (b) 50 and (c) 100 x 106 A m-2.

![](https://assets.underline.io/uploads/markdown_image/1/image/a7e0bd8f7ddc93b92bbc79c9201b5616.jpg)

Fig. 2 Literature comparison of RCP as a function of full-width at half maximum (FWHM) for studied microwires (star symbols) versus amorphous conventional alloys (triangles) and HEAs (squares).

Enhanced Magnetocaloric Response of High-Entropy Alloy Microwires due to Induced Nanocrystals by Current Annealing

Gas liquefaction is an essential aspect for gas storage and transport and its demand will significantly increase as the use of gases such as natural gas as well as H2, He, N2, and O2 become prominent in the development of new technologies (e.g. hydrogen based ones). Systems based on the magnetocaloric effect (MCE) are attracting the interest of the scientific community as they can overcome some of the issues of conventional liquefaction systems [1, 2]. In this work, we studied a series of rare-earth rich RE6Co2Ga (RE = Ho, Dy or Gd) compounds, which shows excellent MCE in the range of H2 and N2 liquefaction temperatures [3]. All the samples crystallize in the Ho6Co2Ga-type crystal structure (Immm space group) without significant presence of impurity phases. The nature of the thermomagnetic transition depends on the rare-earth element, showing metamagnetic anti-to-paramagnetic (AF to PM) transitions for Ho and Dy while a ferro-to-paramagnetic (FM to PM) transition is obtained for Gd. Novel MCE field dependence method [4] and conventional Banerjee's criterion have been used for distinguishing the order of the transition: samples with Ho and Dy are found to undergo first-order phase transition whereas a second order phase transition is observed for the one with Gd. Fig.1 depicts the temperature dependence of the isothermal entropy change (ΔSiso) for a magnetic field change of 0-5 T for Ho and Gd samples. The two compounds show significant values of 10.1 and 9.1 J kg-1 K-1 at 26 and 75 K, close to the liquefaction temperatures of H2 and N2, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/f4b22391b23280e34c4bc60b9a3ec65c.jpg)

The temperature dependence of isothermal entropy change for Ho6Co2Ga and Gd6Co2Ga compounds whose crystal structures belong to Ho6Co2Ga-type.

Cryogenic magnetocaloric effect and thermomagnetic transitions in RE6Co2Ga (RE = Ho, Dy or Gd) compounds

The realization of physical systems whose electronic and magnetic properties can be easily manipulated by playing with valence electrons are very promising from both the fundamental and applied perspectives. Half-metallic ferromagnets are ideal candidates for spintronic applications because of their high spin polarization of charge carriers at the Fermi level [1,2]. High Curie temperature is one of the important precondition of the half-metallic ferromagnets from the application point of view. Co2- based intermetallic Heusler alloys (L21 structure, space group Fm-3m, # 225) are among the most attractive half-metallic systems due to their high Curie temperatures, high spin polarization and the structural similarity to binary semiconductors [1,2]. The Co2FeSi (CFS) system is one such candidate of interest for spintronic applications due to its high Curie temperature crystallizing in the L21 structure but Fermi level falls on the edge of the minority conduction band (in both generalized gradient approximation (GGA) and GGA+U approach) making the system shy from being robust half metallic. High Tc = 1100K and large magnetic moment of 6.00 μB/f.u. is reported in Ref [3]. If one of the Co atom in CFS is replaced by low valence transition metal atom Y = Sc, Ti, V, Cr, Mn, and Fe, alloys with rich and useful properties can be tailored. The quaternary Heusler alloy CoFeMnSi [4] is observed theoretically and experimentally to be spin gapless semiconductor, CoFeCrSi [5] is reported to be half-metallic with some structural disorder, CoFeVSi and CoFeTiSi are reported theoretically to be nearly half-metallic and half-metallic respectively, but both are observed experimentally to show multi-phase behavior in bulk form. The Fermi level lies on the edge of the minority valence band in all Y substituted quaternary Heusler alloys, leading to an unstable half-metallicity. So, as we go from CFS to CoFeYSi, Fermi level is shifted from lower edge of conduction band to upper edge of valence band in minority spin channel which is in accordance to Ref. [2,6]. They have suggested that an expansion of the lattice should shift the Fermi level deeper in energy and the contraction should shift it higher in energy. Therefore, one can expect robust half metallicity with Fermi level exactly at the middle of the band gap for some intermediate Y concentrations in CFS due to the expansion of the lattice when Y with larger atomic radius substitutes for Co. The substitution of Y to Co may be also seen as d-electron deficiency. In this work, we have introduced the substitution of all low valence transition metal atoms Y = Sc, Ti, V, Cr, Mn, and Fe to Co atoms in the parent CFS system, and examined the structural, electronic, magnetic, and mechanical properties of quaternary Heusler compounds Co2-xYxFeSi (0≤x≤1) to get a global overview of the electronic, magnetic and mechanical properties, promising candidates for spintronics applications. All single phase alloys exhibit face centered cubic crystal structure with a strong tendency towards L21 ordering, as corroborated by X-ray diffraction. The low-temperature saturation magnetic moments agree fairly well with our theoretical results and also obey the Slater-Pauling rule, a prerequisite for half metallicity. Fig.1 shows the linear decrease of the spontaneous magnetizations measured at 2K with the valence electron counts per formula units with element Y = Ti, V, Cr, Mn, Fe, and Co in Co2-xYxFeSi (x = 0.50). All alloys are soft ferromagnets with high Curie temperatures, ranging from 700K to 1100K, allowing for applications at room temperature and above. The Curie temperatures are observed to vary almost linearly with the saturation magnetic moment which is also expected in half-metallic systems. First-principles calculations also predicted finite band gap in the minority spin channel for most of the alloys in Co2-xYxFeSi series. Fig. 2 shows the calculated density of states (DOS) plots using GGA approach for majority and minority spin channels of Co2-xMnxFeSi (0≤x≤1) alloys, where the Fermi level is represented by the zero energy. It can be seen clearly that the system exhibits half-metallic behavior after Mn substitution. In the case of parent compound CFS, there is significant amount of DOS at the Fermi level on both the spin channels. After Mn substitution, the Fermi level is observed to shift deeper in energy-levels and falls at the middle of the energy gap on spin down channel for x = 0.50. Further increase of Mn content shifts the Fermi level towards the lower edge of energy gap due to lattice expansion. But, still Fermi level lies within energy gap making the system Half-metallic. In addition, conduction band and valence band in majority spin channel touch each other at Fermi level in x = 1, making the system spin gapless semiconductor. The energy gap is observed to increase with the increase of Mn content. Although, the calculated minority spin gap is the highest for x = 1, the half-metallic gap is greater for x = 0.50. Relatively high mechanical hardness values among the reported Heusler alloys are also observed, approaching 16 GPa for the most Ti-rich material [6-8].

**References:**

1. C. Felser, G. H. Fecher, and B. Balke, Angewandte Chemie International Edition, 46, 668 (2007). 2. I. Galanakis, P. Dederichs and N. Papanikolao, Physical Review B, 66, 174429 (2002). 3. E. Fischer, J. Karel and S. Fabbrici, Physical Review B, 94, 024418 (2016). 4. L. Bainsla, A.I. Mallick and M.M. Raja, Physical Review B, 91, 104408 (2015). 5. Y. Jin, P. Khareland P. Lukashev, Journal of Applied Physics, 120, 053903 (2016). 6. R. Mahat, S. KC and U. Karki, Physical Review B, Submitted (2021). 7. R. Mahat, S. KC and D. Wines, Journal of Alloys and Compounds, 830, 154403 (2020). 8. R. Mahat, S. KC and D. Wines, Journal of Magnetism and Magnetic Materials, 521, 167398 (2021).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7c947ceb5f0d173267903a665062a366.jpg)
Fig.1. The saturation magnetic moment versus valence electron counts per formula units with element Y = Ti, V, Cr, Mn, Fe, and Co in Co2-xYxFeSi (x = 0.50), both experimental and expected from Slater Pauling rule for half metals. The black data points represent reported literature values [3].

![](https://assets.underline.io/uploads/markdown_image/1/image/42867fe7839357c6b915951bb21bee55.jpg)
Fig.2. Spin polarized total DOS for Co2-xYxFeSi (Y = Mn, 0≤x≤1). Number of states is scaled with respect to one formula unit.

 Effect of mixing the low-valent transition metal atoms Y = Sc, Ti, V, Cr, Mn and Fe on the properties of quaternary Heusler compounds Co2-xYxFeSi (0≤x≤1)

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

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

**References:**

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

**Images:**

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

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

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

**References:**

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

**Images:**

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

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

NOB: Magnetocaloric Materials I

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