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The RTX compounds, where R is a 4&lt;i&gt;f&lt;/i&gt;-metal, T and X are &lt;i&gt;d&lt;/i&gt;- and &lt;i&gt;p&lt;/i&gt;-elements, exhibit various physicochemical properties and have potential for practical application [1]. The GdFeSi, GdTiSi and GdMnSi compounds crystallize into the same tetragonal CeFeSi (&lt;i&gt;P4/nmm&lt;/i&gt;)-type structure [1,2]. This structure is composed of alternating (001) layers with the sequence: Gd-Si-T2-Si-Gd-Gd-Si-T2-Si-Gd (T = Fe, Co, Ti, Mn). This is why the exchange interactions between atoms Gd–Gd, Gd–T, T–T in GdTSi depend on the lattice parameter &lt;i&gt;c&lt;/i&gt;, whereas interaction T–T depends on the lattice parameter &lt;i&gt;a&lt;/i&gt; as well. The hybridization of Si &lt;i&gt;p&lt;/i&gt; and T 3&lt;i&gt;d&lt;/i&gt; states causes filling of the 3&lt;i&gt;d&lt;/i&gt; band and results in the absence of magnetic moment of T = Fe or Co in the GdTSi compound [1-5]. Mn is a unique example of the 3&lt;i&gt;d&lt;/i&gt;-transition metal T with a magnetic moment in the GdTSi compounds. Significant changes in the magnetic and structural parameters of these compounds were observed upon a mutual partial substitution of &lt;i&gt;d&lt;/i&gt;-metals.&lt;br/&gt;In this work, the intermetallic compounds GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si, &lt;i&gt;x&lt;/i&gt;=0-0.95 with a tetragonal crystal structure of the CeFeSi (&lt;i&gt;P4/nmm&lt;/i&gt;)-type have been studied. It is shown in Fig.1 that the lattice parameter &lt;i&gt;c&lt;/i&gt; and the Curie temperature &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; increase, whereas the lattice parameter &lt;i&gt;a &lt;/i&gt;is almost unchanged in the GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si system when the concentration of Mn increases. The similar variations of the lattice parameters and &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; were earlier obtained for the GdFe&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si system [3], although &lt;i&gt;c&lt;/i&gt; and &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; are noticeably smaller as compared with GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si, whereas &lt;i&gt;a &lt;/i&gt;is about the same. Hence, an increase of &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; in the systems is caused by short-range Mn-Mn exchange interactions in the basal plane, whereas higher &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; in GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si is caused by stronger indirect exchange interactions Gd-Gd.&lt;br/&gt;The increase in the interatomic distances along the &lt;i&gt;c&lt;/i&gt; axis due to large Ti substitution atoms should weaken the Gd-Gd, Gd-T and T-T exchange interactions and should decrease &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; in GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si as compared with GdFe&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si. At the same time, the partial substitution of Ti for Fe or Mn decreases a number of the 3&lt;i&gt;d&lt;/i&gt; “spin-down” electrons in the system, because Ti, Mn and Fe atoms have 2, 5 and 6 of the 3&lt;i&gt;d&lt;/i&gt; electrons, respectively. As a result, a number of the 3&lt;i&gt;d &lt;/i&gt;electrons with “spin up” non-compensated by the 3&lt;i&gt;d&lt;/i&gt; electrons with “spin down” increases. Owing to this, indirect exchange interactions between Gd ions become stronger, because they are realized through polarization of the conduction electrons. The difference between the numbers of the 3&lt;i&gt;d&lt;/i&gt; electrons for Ti (2) and Mn (5) or Fe (6) is less for the compositions &lt;i&gt;x &lt;/i&gt;&amp;gt; 0.5, where the concentration of Mn prevails, than for the compositions &lt;i&gt;x&lt;/i&gt; &amp;lt; 0.5, where the concentration of Fe prevails. As a result, &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; for GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si exceeds &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; for GdFe&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si by 10-15 K for the compounds with &lt;i&gt;x&lt;/i&gt;&amp;gt; 0.5 and by 50-70 K for the compounds with &lt;i&gt;x&lt;/i&gt; &amp;lt;0.5.&lt;br/&gt;Fig.2 shows that the saturation magnetization &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;sat&lt;/sub&gt; decreases non-monotonically in the GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si system with a minimum at intermediate compositions. Usually, the R–T intermetallic compounds with a heavy rare earth element R are characterized by strong negative R–T exchange interaction [1]. From this point of view, one should expect the antiparallel arrangement of Gd and Mn moments and a linear decrease in magnetization in the GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si system with an increase in Mn concentration. It is obvious that this model cannot explain the existence of the minimum on the dependence &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;sat.&lt;/sub&gt;(&lt;i&gt;x&lt;/i&gt;). A similar change of &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;sat.&lt;/sub&gt;(&lt;i&gt;x&lt;/i&gt;) with a minimum was published for the GdFe&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si system [4]. It was shown that the GdMnSi compound is characterized by strong exchange interactions inside the Gd and Mn subsystems and weaker Gd–Mn interaction, since the atoms of different types are stacked in isolated (001) layers [2,6]. As a result, a non-collinear ferrimagnetic structure is formed in GdMnSi in which the moments of Gd ions are oriented along the tetragonal axis of the compound and the moments of Mn ions are oriented at an angle to it. Apparently, a similar structure exists in the GdFe&lt;sub&gt;1-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si and GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si systems. Variations of Mn concentration or strength of external magnetic field can produce an essential change in the relative orientation of magnetic moments of the Gd and Mn sublattices and non-monotonic variation of &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;sat.&lt;/sub&gt;(&lt;i&gt;x&lt;/i&gt;).&lt;br/&gt;The isothermal magnetic entropy change -&lt;i&gt;Δ&lt;/i&gt;&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;M&lt;/sub&gt; (i.e. the magnetocaloric effect MCE) was calculated from the magnetization isotherms &lt;i&gt;M&lt;/i&gt;(&lt;i&gt;H&lt;/i&gt;) using the well-known Maxwell relation [1]. The peak value of -&lt;i&gt;Δ&lt;/i&gt;&lt;i&gt;S&lt;/i&gt;&lt;sub&gt;M&lt;/sub&gt; decreases with the appearance Mn in the GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si system and varies within a narrow range of 1.2-1.6 J/kgK at 17 kOe field for all Mn contents. At the same time, &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; varies in a wide range around room temperature: from 220 to 360 K. Thus, the MCE of the GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si compounds can be of practical interest.&lt;br/&gt;Acknowledgements&lt;br/&gt;Support by RSF (Project No. 18-72-10098) is acknowledged.

**References:**

[1] S. Gupta and K.G. Suresh, J. Alloys Comp., Vol. 618, p.562 (2015)&lt;br/&gt;[2] R. Welter, G. Venturini and B. Malaman, J. Alloys Comp., Vol. 189, p.49 (1992)&lt;br/&gt;[3] S.A. Nikitin, T.I. Ivanova and I.A. Tskhadadze, J. Alloys Comp., Vol. 280, p.16 (1998)&lt;br/&gt;[4] S.A. Nikitin, T.I. Ivanova and I.A. Tskhadadsze, Acta Phys. Pol., Vol. A 91, p.463 (1997)&lt;br/&gt;[5] M. Napoletano, F. Capera and P. Manfrinetti, J. Mater. Chem., Vol. 10, p.1663 (2000)&lt;br/&gt;[6] I.A. Ovtchenkova, S.A. Nikitin and T.I. Ivanova, J. Alloys Comp., Vol. 451, p.450 (2008)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9de671cd9d1da85ef442536dd7b098b7.jpg)
Fig.1. Dependences of the lattice parameters &lt;i&gt;a&lt;/i&gt; (■) and &lt;i&gt;c&lt;/i&gt; (●) and the Curie temperature &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; (△) of the GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si compounds versus Mn content.

![](https://assets.underline.io/uploads/markdown_image/1/image/182009ac8016f05e56d7616efee6545a.jpg)
Fig.2. Concentration dependence of the saturation magnetization &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;sat.&lt;/sub&gt; measured on free powder samples of the GdTi&lt;sub&gt;0.05&lt;/sub&gt;Fe&lt;sub&gt;0.95-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Mn&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;Si compounds at &lt;i&gt;T = &lt;/i&gt;4 K. Points (●) – experiment, line – interpolation.

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 Substitution of Fe by Ti and Mn in GdFeSi

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The RTX compounds, where R is a 4f-metal, T and X are d- and p-elements, exhibit various physicochemical properties and have potential for practical application [1]. The GdFeSi, GdTiSi and GdMnSi compounds crystallize into the same tetragonal CeFeSi (P4/nmm)-type structure [1,2]. This structure is composed of alternating (001) layers with the sequence: Gd-Si-T2-Si-Gd-Gd-Si-T2-Si-Gd (T = Fe, Co, Ti, Mn). This is why the exchange interactions between atoms Gd–Gd, Gd–T, T–T in GdTSi depend on the lattice parameter c, whereas interaction T–T depends on the lattice parameter a as well. The hybridization of Si p and T 3d states causes filling of the 3d band and results in the absence of magnetic moment of T = Fe or Co in the GdTSi compound [1-5]. Mn is a unique example of the 3d-transition metal T with a magnetic moment in the GdTSi compounds. Significant changes in the magnetic and structural parameters of these compounds were observed upon a mutual partial substitution of d-metals. In this work, the intermetallic compounds GdTi0.05Fe0.95-xMnxSi, x=0-0.95 with a tetragonal crystal structure of the CeFeSi (P4/nmm)-type have been studied. It is shown in Fig.1 that the lattice parameter c and the Curie temperature TC increase, whereas the lattice parameter a is almost unchanged in the GdTi0.05Fe0.95-xMnxSi system when the concentration of Mn increases. The similar variations of the lattice parameters and TC were earlier obtained for the GdFe1-xMnxSi system [3], although c and TC are noticeably smaller as compared with GdTi0.05Fe0.95-xMnxSi, whereas a is about the same. Hence, an increase of TC in the systems is caused by short-range Mn-Mn exchange interactions in the basal plane, whereas higher TC in GdTi0.05Fe0.95-xMnxSi is caused by stronger indirect exchange interactions Gd-Gd. The increase in the interatomic distances along the c axis due to large Ti substitution atoms should weaken the Gd-Gd, Gd-T and T-T exchange interactions and should decrease TC in GdTi0.05Fe0.95-xMnxSi as compared with GdFe1-xMnxSi. At the same time, the partial substitution of Ti for Fe or Mn decreases a number of the 3d “spin-down” electrons in the system, because Ti, Mn and Fe atoms have 2, 5 and 6 of the 3d electrons, respectively. As a result, a number of the 3d electrons with “spin up” non-compensated by the 3d electrons with “spin down” increases. Owing to this, indirect exchange interactions between Gd ions become stronger, because they are realized through polarization of the conduction electrons. The difference between the numbers of the 3d electrons for Ti (2) and Mn (5) or Fe (6) is less for the compositions x &gt; 0.5, where the concentration of Mn prevails, than for the compositions x &lt; 0.5, where the concentration of Fe prevails. As a result, TC for GdTi0.05Fe0.95-xMnxSi exceeds TC for GdFe1-xMnxSi by 10-15 K for the compounds with x&gt; 0.5 and by 50-70 K for the compounds with x &lt;0.5. Fig.2 shows that the saturation magnetization Msat decreases non-monotonically in the GdTi0.05Fe0.95-xMnxSi system with a minimum at intermediate compositions. Usually, the R–T intermetallic compounds with a heavy rare earth element R are characterized by strong negative R–T exchange interaction [1]. From this point of view, one should expect the antiparallel arrangement of Gd and Mn moments and a linear decrease in magnetization in the GdTi0.05Fe0.95-xMnxSi system with an increase in Mn concentration. It is obvious that this model cannot explain the existence of the minimum on the dependence Msat.(x). A similar change of Msat.(x) with a minimum was published for the GdFe1-xMnxSi system [4]. It was shown that the GdMnSi compound is characterized by strong exchange interactions inside the Gd and Mn subsystems and weaker Gd–Mn interaction, since the atoms of different types are stacked in isolated (001) layers [2,6]. As a result, a non-collinear ferrimagnetic structure is formed in GdMnSi in which the moments of Gd ions are oriented along the tetragonal axis of the compound and the moments of Mn ions are oriented at an angle to it. Apparently, a similar structure exists in the GdFe1-xMnxSi and GdTi0.05Fe0.95-xMnxSi systems. Variations of Mn concentration or strength of external magnetic field can produce an essential change in the relative orientation of magnetic moments of the Gd and Mn sublattices and non-monotonic variation of Msat.(x). The isothermal magnetic entropy change -ΔSM (i.e. the magnetocaloric effect MCE) was calculated from the magnetization isotherms M(H) using the well-known Maxwell relation [1]. The peak value of -ΔSM decreases with the appearance Mn in the GdTi0.05Fe0.95-xMnxSi system and varies within a narrow range of 1.2-1.6 J/kgK at 17 kOe field for all Mn contents. At the same time, TC varies in a wide range around room temperature: from 220 to 360 K. Thus, the MCE of the GdTi0.05Fe0.95-xMnxSi compounds can be of practical interest. Acknowledgements Support by RSF (Project No. 18-72-10098) is acknowledged.

**References:**

[1] S. Gupta and K.G. Suresh, J. Alloys Comp., Vol. 618, p.562 (2015) [2] R. Welter, G. Venturini and B. Malaman, J. Alloys Comp., Vol. 189, p.49 (1992) [3] S.A. Nikitin, T.I. Ivanova and I.A. Tskhadadze, J. Alloys Comp., Vol. 280, p.16 (1998) [4] S.A. Nikitin, T.I. Ivanova and I.A. Tskhadadsze, Acta Phys. Pol., Vol. A 91, p.463 (1997) [5] M. Napoletano, F. Capera and P. Manfrinetti, J. Mater. Chem., Vol. 10, p.1663 (2000) [6] I.A. Ovtchenkova, S.A. Nikitin and T.I. Ivanova, J. Alloys Comp., Vol. 451, p.450 (2008)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9de671cd9d1da85ef442536dd7b098b7.jpg)
Fig.1. Dependences of the lattice parameters a (■) and c (●) and the Curie temperature TC (△) of the GdTi0.05Fe0.95-xMnxSi compounds versus Mn content.

![](https://assets.underline.io/uploads/markdown_image/1/image/182009ac8016f05e56d7616efee6545a.jpg)
Fig.2. Concentration dependence of the saturation magnetization Msat. measured on free powder samples of the GdTi0.05Fe0.95-xMnxSi compounds at T = 4 K. Points (●) – experiment, line – interpolation.

poster

The precise study of the bonding in materials is an important part of material characterization. The Maximum Entropy Method (MEM) is a powerful tool for deriving accurate electron density distribution in crystalline materials using experimental data. The MEM provides us with the least biased deduction, which is compatible with certain given information. The bonding nature and the distribution of electrons in the bonding region can be clearly visualized using this technique. MEM electron densities are always positive and even with the limited number of data, one can evaluate reliable electron densities resembling true densities. In this present work, the attention is focused on the growth, structural, and electron density distribution of Gd3Fe5-xAlxO12 (0 ≤ x ≤ 1) using X-ray powder data. Gd3Fe5-xAlxO12; x = 0.0, 0.25, 0.50 and 1.0 samples were synthesized via auto combustion method and heat-treated in air at 1100oC for 12 h. The phase identification and lattice parameter of the powders performed using X-ray diffraction data. The Rietveld analysis was performed for the present analysis, which proves the synthesized material of Gd3Fe5-xAlxO12 (0 ≤ x ≤ 1) stays in high-crystalline with single-phase garnet structure, the structural and profile parameter were compared with the reported results from JCPDS-48-0077. The Rietveld analysis was performed using JANA 2000 software package, the results show that the lattice parameters and the cell volume decrease with the increasing the Al, this is clearly evidencing the Al content is replacing the Fe. From this analysis, we observed that a gradual shift in the peaks from the lower angle to the higher angle as compared to the pure Gd3Fe5O12. The lattice parameters for Gd3Fe5-xAlxO12 decreases from 12.50A to 12.44A due to smaller ionic radii of Al3+ ion (0.535A) replacing Fe3+ ions (0.645A). The atomic site occupancy and bond distance analysis for each site were derived from Rietveld refinement for Gd3Fe5-xAlxO12, the Al is preferred to the tetrahedral site for x ≤ 0.5 and prefers both sites; tetrahedral and octahedral thereafter. The structure factors from the Rietveld analysis were further taken to determine the electron density distribution analysis by MEM method. The bonding nature and radii of atoms/ions and interaction between the atoms were clearly analyzed and represented by 3D, 2D, and 1D MEM maps. The mid bond electron densities between atoms were analyzed. The two-dimensional MEM electron density maps on the (001) and (202) planes, and the one-dimensional electron density profiles along Fe-O, Gd-O, and O-O directions were calculated. From this analysis, the substitution of Al3+ ions actually reduces the lattice parameter and volume of the Gd3Fe5-xAlxO12. The 2D map shows the depletion of charge density in the valence regions are clearly seen. Our study suggests that the Al3+ doped Gd3Fe5O12 nano-materials could exhibit interesting electronic properties for data storage applications.

**References:**

1. Lassri, H., Hlil, E. K., Prasad, S., & Krishnan, R. (2011). Magnetic and electronic properties of nanocrystalline Gd3Fe5O12 garnet. Journal of solid state chemistry, 184(12), 3216-3220. 2. Nakamoto, R., Xu, B., Xu, C., Xu, H., & Bellaiche, L. (2017). Properties of rare-earth iron garnets from first principles. Physical Review B, 95(2), 024434. 3. Ali, K. S., Saravanan, R., Israel, S., & Arda, L. (2010). Localized ferromagnetic charge ordering through charge density analysis in nano sized diluted magnetic semiconductor Co2+: ZnO. Physica B: Condensed Matter, 405(7), 1763-1769. 4. Ali, K. S., Saravanan, R., Pashchenko, A. V., & Pashchenko, V. P. (2010). Local distortion in Co-doped LSMO from entropy-maximized charge density distribution. Journal of Alloys and Compounds, 501(2), 307-312. 5. Saravanan, R., & Rani, M. P. (2011). Metal and alloy bonding-an experimental analysis: Charge density in metals and alloys. Springer Science & Business Media.

**Images:**

 Structural and Electronic properties on Gd3Fe5-xAlxO12 (x= 0.25, 0.5, 1.00) using Rietveld, Maximum Entropy Method (MEM)

The family of manganese oxides with the general formula R1-xAxMnO3 (R=lanthanide and A=divalent alkaline earth) has a non-negligible potential in magnetic cooling particularly because of the high chemical stability and interesting magnetocaloric properties at room temperature [1]. In this work, we report a detailed study of the thermodynamic performance of Pr0.6Sr0.4MnO3 in a functional magnetic cooling system up to the theoretical limit of its magnetocaloric effect. In this context, a one-dimensional numerical model of the AMR cycle is developed, while the required magnetocaloric properties of the oxide are calculated in the framework of Mean Field Theory (MFT). The obtained results are deeply analyzed and then compared with the reference Gadolinium (Gd) metal. Moreover, it is revealed that using Pr0.6Sr0.4MnO3 as refrigerant requires high magnetic fields to generate reasonable temperature spans for application. Under a magnetic field of 8 T, the studied oxide can generate an AMR temperature span of 33 K. However, such a span can be achieved by employing Gd and using only a magnetic field source of 1.45 T. The thermodynamic efficiency was evaluated by directly considering the involved magnetic forces between the Pr0.6Sr0.4MnO3 regenerator and the magnetic field source. The associated magnetic work is numerically calculated by using Altair Flux 3D software. Particularly, it was found that the coefficient of performance (COP) can be enhanced by a factor of two when balancing magnetic forces (Fig. 1) despite of the moderate magnetocaloric effect shown by Pr0.6Sr0.4MnO3 under practical fields (1 to 2 T). On the other hand, the hidden thermodynamic performances of this compound are also pointed out by investigating its magnetocaloric properties in the theoretical limit zone. In this way, our calculations unveil that is possible to reach cold source temperatures under -22°C even when using helium as heat transfer fluid (Fig. 2). Finally, a magnetic cooling device working with Pr0.6Sr0.4MnO3 as refrigerant and fully powered by solar cells is proposed.

**References:**

[1] M. Balli, S. Jandl, P. Fournier, and A. Kedous-Lebouc, Appl. Phys. Rev. 4, 021305 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c8bd35af86f03d8a8875379d767e6ec9.jpg)
Fig. 1 The simulated magnetic forces in the case of one and two separated regenerators of Pr0.6Sr0.4MnO3.

![](https://assets.underline.io/uploads/markdown_image/1/image/1c021cfc7ac84b35b464f05f9437c523.jpg)
Fig. 2 Temperature evolution of the hot and cold ends as a function of the number of cycles for using helium as transfer fluid

 On the real potential of R1-xAxMnO3 oxides in magnetic cooling: Pr0.6Sr0.4MnO3 as a case of study

The materials that exhibit mutual control of more than one property by external stimuli such as magnetic, electric and stress fields are known as multifunctional material. They are useful to design smart sensors and can be extended as a functional refrigerant for cooling. The magnetic refrigerator is an alternative to the conventional refrigerators as they do not emit toxic greenhouse gases to the environment. However, the product cost of a magnetic refrigerator is expensive due to the raw material and magnetic components required to achieve the maximum entropy change at a given magnetic field strength (≤1.5 T). Assuming the combination of electric and magnetic properties may yield adiabatic temperature change at low (magnetic/electric) field, the piezoelectric/magnetic nanocomposites are proposed. Poly(methyl methacrylate)/Poly(vinylidenefluoride-co-hexafluoropropylene) (PMMA/PVDF-HFP) blend and PMMA/PVDF-HFP/Zn0.5Cu0.5Fe2O4 flexible nanocomposites were fabricated by solution casting method. Pristine polymer blend and PMMA/PVDF-HFP/ferrite nanocomposite are having 67 and 62% of F(b), respectively. Zn0.5Cu0.5Fe2O4 and PMMA/PVDF-HFP/Zn0.5Cu0.5Fe2O4 nanocomposite show superparamagnetic nature with the saturation magnetization of 44 and 5.3 emu/g, respectively. The composite film is thermally stable up to 753 K and later it shows 80% of weight loss. The magnetic entropy change (DSM) of Zn0.5Cu0.5Fe2O4 and PMMA/PVDF-HFP/Zn0.5Cu0.5Fe2O4 show interesting table-like flat variation with respect to magnetic field (0 to 40 kOe) and temperature (100 to 400 K). The DSM (refrigerant capacity) at 300 K is found to be -0.69 (293 J/kg) and -0.094 (40 J/kg) J/kg/K for Zn0.5Cu0.5Fe2O4 and PMMA/PVDF-HFP/Zn0.5Cu0.5Fe2O4, respectively. Ferroelectric polarization change as a function of electric field is analysed at room temperature. The composite film exhibiting both magnetism and ferroelectricity is proved and would be attractive to design different compositions to increase the temperature variation for cooling devices.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/db2e5a1e5dec581473008e717fb6b89a.jpg)
Figure 1 (A) X-ray diffraction patterns, (B) and (C) M-H hysteresis loops of Zn0.5Cu0.5Fe2O4 and PP/Zn0.5Cu0.5Fe2O4 nanocomposite respectively.

 Multiferroic Electroactive Polymer Blend/Ferrite Nanocomposite Film for Cooling Devices

The current interest in developing solid-state refrigeration devices has encouraged the investigation of caloric effects linked to first-order phase transitions in different families of solids [1]. Among them, (Ni, Mn)-based Heusler-type magnetic shape memory alloys have deserved particular attention due to their multicaloric nature [2]. For properly chosen compositions, martensitic transformation (MT) in Ni-Fe-Ga alloys appears around room temperature (RT) [1]. This, together with their good mechanical properties in comparison with other (Ni,Mn)-based alloys (improved with the precipitation of γ phase [3]), and the facts that with the partial replacement of Fe by Mn in the Ni55Fe19Ga26 alloy γ phase remains in a low concentration, increases the entropy of the MT, not significantly modifying the MT temperature [3], motivated present investigation. Two bulk Ni55Fe11Mn7Ga27 samples were prepared from pure elements (≥ 99.9 %) by arc-melting and spark plasma sintering (SPS) (bulk and SPS samples, respectively), and their phase constitution, as well as magnetocaloric (MC) and elastocaloric (eC) effects studied across the MT. The SPS sample was a dense disc (ρ ≈ 8.4 g.cm-3; ∼ 99 % in respect of theoretical), with diameter and height of 15 and 2.2 mm, sintered from a powdered arc-melted ingot at constant pressure of 30 MPa in a Labox-210 SPS system. The time evolution of vertical displacement and temperature during the process is given in Fig. 1(a). Samples received homogenization annealing at 1273 K for 24 h, followed by a chemical ordering treatment at 773 K (1 h). Start and finish temperatures of the structural transition were determined from the 5 and 95 %, respectively, of the DSC peak area. RT phase constitution was determined by X-ray diffraction (XRD). As Fig. 1(b) shows, the structural transition for both samples is close to RT with similar temperatures. This highlights the effectiveness of SPS technique for consolidating (Ni-Fe-Ga)-based alloys. XRD patterns, shown in Figs. 1(c) and (d), respectively, were obtained with the X-ray beam impinging on a plane perpendicular to the gradient during solidification and on the surface of the sintered disc. In both patterns, a L21-type austenite (AST) is the major phase, while cubic γ phase [4] is also detected (∼ 6 %vol.). However, notice that the peak intensities in the XRD pattern for the SPS sample correspond to an isotropic polycrystal, whereas for the bulk arc melted one AST grains preferentially grow with the [1 0 0] direction oriented along the thermal gradient during solidification. Partial preferential and non-preferential grain orientation in both samples was confirmed by SEM observations (not shown). Magnetization measurements were done by VSM in a PPMS Dynacool system. M(T) curves, under 5 mT and 5 T following zero-field-cooling (ZFC) and field-cooling (FC) regimens (1.0 Kmin-1), are depicted in Fig. 2(a). The magnetic entropy change ΔSM was estimated from the Maxwell relation through the reverse MT from a set of M(T) curves (shown in Fig. 2(b)), measured up to an applied magnetic field μ0Hmax of 5 T. As shown in Fig. 2(c), bulk sample exhibits a moderate │ΔSM│max value of 8.2 (12.9) Jkg-1K-1 under μ0ΔHmax = 2 (5) T (tough │ΔSM│max values measured are the largest reported for alloy studied [3]). The eC effect adiabatic temperature change ΔTadme was determined in a home-made facility under a compression uniaxial load change of 120 MPa for parallelepiped-shaped samples cut from the bulk and SPS samples; uniaxial stress for the bulk sample was applied along thermal gradient during solidification. Fig. 2(d) gives the ΔTadme(T) curves for both samples loading and unloading the uniaxial stress. The bulk sample exhibits a │ΔTadme│max of 2.4 K at a load removal of 120 MPa, whereas this magnitude significantly decreases for the SPS sample. This result agrees with the around 1/3 reduction of the eC effect expected for the direction [1 1 0] [5,6]. Hence, the above-mentioned partial crystallographic texture and isotropic nature of the samples, explain the significant difference observed in the eC effect value. In summary, apart from probing the efficacy of SPS technique for the shaping and consolidation of Ni-Fe-Ga alloys exhibiting similar phase transformation temperatures than those obtained for the bulk sample, the MC and eC effects were assessed for bulk samples of the Heusler alloy Ni55Fe11Mn7Ga27. Whereas the MC effect is moderate in comparison with the reported for (Ni-Mn-X)-based alloys (X= Ga, In, Sn, Sb), our results underline their good mechanical strength and the relevant role of crystallographic texture on the eC effect.

**References:**

[1] Ll. Mañosa, A. Planes, Adv. Mater. 29 (2017) 1603607. [2] Ll. Mañosa, A. Planes, Phil. Trans. R. Soc. A 374 (2016) 20150310. [3] S. Kumar Sarkar, A. Biswas, P.D. Babu, S.D. Kaushik , A. Srivastava, V. Siruguri, M. Krishnan, J. Alloys Compd. 586 (2014) 515–523. [4] T. Omori, N. Kamiya, Y. Sutou, K. Oikawa, R. Kainuma, K. Ishida, Mater. Sci. Engin. A 378 (2004) 403–408. [5] F. Xiao, M. Jin, J. Liu, X. Jin, Acta Mater. 96 (2015) 292–300. [6] F. Hernández-Navarro, J.P. Camarillo-Garcia, C.O. Aguilar-Ortiz, H. Flores-Zúñiga, D. Ríos, J.G. González, P. Álvarez-Alonso, Appl. Phys. Lett. 112 (2018) 164101.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/01c19f0fdf5abb60c13512568d4f30f1.jpg)
Fig. 1. (a) Vertical displacement and temperature versus time along the SPS process. (b) DSC curves for bulk and SPS samples (10 K.min-1). Starting and finishing MT temperatures for the bulk (SPS) sample were MS= 276 (278) K, Mf= 269 (262) K, AS= 277 (279) K, and Af= 286 (290) K. (c) and (d) indexed XRD patterns for bulk and SPS samples, respectively (CuKα).

![](https://assets.underline.io/uploads/markdown_image/1/image/62373c7b9f1fcd916d158bd34a413bff.jpg)
Fig 2. ZFC and FC M(T) curves under 5 mT and 5 T across the structural transition (a), isofield M(T) curves under fields from 1 to 5 T (b), and DSM(T) curves (c) through the reverse MT for the bulk arc melted alloy. (d) ΔTadme(T) for both samples under a load and unload applied stress of 120 MPa. Inset: ΔTadme as a function of time at 297 K for the bulk sample.

 Elastocaloric and magnetocaloric effects through the martensitic transformation in bulk Ni55Fe11Mn7Ga27 alloys produced by arc-melting and spark plasma sintering

Recently so-called shape-memory ferromagnets based on Heusler alloys Ni-Mn-Z (Z = Ga, In, Sn, Sb) began to be considered as a promising materials for magnetic cooling technology. These alloys can exceed compounds with gadolinium in the value of the magnetocaloric effect (MCE) for magnetic field of the same magnitude, because the giant values of the MCE are achieved in them due to the structural transformation accompanying the magnetic transition. The electrical and magnetic properties of the alloy are closely related with the state of its microstructure, which can be changed using various methods of intense plastic deformation (e. g. equal channel angular pressing, intense torsional plastic deformation) or thermobaric treatment (TBT) which is the processing of materials under conditions of high temperature (up to 2000 K) and high quasi-hydrostatic pressure (up to 10 GPa). Ingots of Ni45Mn44In11 alloy were prepared by arc melting in an inert atmosphere and subsequently subjected to annealing at 1100 K for 24 h followed by furnace cooling. The temperature dependence of the electrical resistivity ρ(T) were measured by the standart method. The magnetic properties were measured using an MPMS XL7 (Quantum Design) SQUID magnetometer. The magnetic properties were measured in magnetic fields of up to 70 kOe in the temperature range 150-330 K. Thermobaric treatment has a significant effect on both electrical (changing the type of temperature dependence of electrical resistivity from “semiconductor” to “metallic”) and magnetic properties of the Ni45Mn44In11 alloy. In addition, as a result of TBT, the maximum value of electrical resistivity increases in 1,7 times. Despite this the value of the entropy change ΔS before and after TBT practically was not changed (ΔS ≈ 3.6 J/(kg*K)), but its maximum shifted along the temperature scale from 200 K to 300 K. The results of this work were obtained within the state assignment of Minobrnauki of Russia (theme “Spin” No. AAAA-A18-118020290104-2) and “New functional materials for promising technologies: synthesis, properties, spectroscopy and computer simulation” (No. AAAA-A19-119031890025-9), supported in part by the Government of Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).

**References:**



**Images:**

 Magnetocaloric effect in the alloy Ni45Mn44In11 subjected to the thermobaric treatment

Heusler alloys are promising candidates for micro-magnetic cooling applications thank their desirable behavior. The possibility of tuning the structural transformation temperature by changing the stoichiometry of compounds is one of the most favorable properties in the presented group of alloys. Modulation of valence electron concentration ratio can be used to produce microwires with the required transformation temperature. Preparation by the Taylor-Ulitovsky technique allows easy and fast production of microwires with protective glass coating. In this work, Heusler alloys in the form of glass-coated microwires with different valence electron concentration ratio (e/a) are analyzed. The effect of e/a tuning on martensitic transformation temperature has been studied using indirect magnetocaloric measurements and their proper analysis. Modified Arrott plot and critical exponent analysis point to the fact that the series of Ni2FeGa microwires belong to the same universality. Hence transformation temperature in this series of alloys has been estimated from transformation temperature vs. e/a dependence using the interpolation method. This research was supported by Slovak Grant Agency VEGA 1/0053/19, Slovak Grant Agency grant number APVV-16-0079.

**References:**

V. Franco and A. Conde, International Journal of Refrigeration, Vol. 33(3), p. 465–473 (2010) A. Kharrat and W. Boujelben, Journal of Low Temperature Physics, Vol. 197, p. 357–378 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a857e0e0bd2c19692c000c28b9513ebf.jpg)

 Modified Arrott plot and critical exponent study on series of magnetocaloric Ni2FeGa based Heusler glass-coated microwires

Heusler alloys X2YZ are well-known materials for their various properties which depend on their chemical composition and structure [1]. Their unique features such as shape memory effect, magnetocaloric effect, superconductivity, or spin polarisation have been observed and well described in the form of bulk, rapidly quenched ribbons, glass-coated microwires, or thin films [2]. Therefore, one fundamental question arises: whether the peculiar properties of Heusler alloys will also remain in the nanoscale? There are several technology areas that may be enhanced using Heusler alloys, especially in the field of spintronics, sensors and actuators, biological application based on hypo- or hyperthermia, or drug delivery [3]. The preparation of a large amount of Heusler alloys in the form of nanomaterials with a well-defined shape remains still a challenge. Here, one of the best possible methods consists of the fast and straightforward electrochemical approach [4-5]. With the presented template-assisted deposition using nanoporous anodic alumina membrane, it is possible to prepare a considerable amount (109 nanowires/cm2) of nanodisks or 1D nanowires with uniform morphology and chemical composition. Thanks to the possibility of co-deposition of various metals such as Fe, Co, Ni, Mn, In, Ga, Sn, etc., many types of ternary and quaternary Heusler alloys can be prepared via electrochemical deposition in the various form [6]. We present the possibility of the preparation of Heusler nanowires via electrochemical deposition in nanoporous anodic alumina template with well-defined shape and morphology. Depending on the chemical composition, the prepared Heusler nanowires show different physical properties such as high spin polarisation (Co2FeZ based Heusler alloys) and magnetocaloric or shape memory effect (Ni2FeZ-based). Electrodeposited Co2FeSn nanowires with a diameter of 60 nm and length 10 μm exhibit B2 disordered phase, high curie temperature (&gt;1000 K) and easy magnetization axis parallel to the nanowires axis. Point Contact Andreev Reflection spectroscopy (PCAR) performed with Nb superconductive tip revealed high spin polarisation up to 100 %. The presented approach allows the preparation of promising nano scaled Heusler alloys suitable for applications in spintronics or high-density magnetic data recording [7]. On the other hand, Ni2FeGa-based Heusler alloys are well known as shape memory or magnetocaloric materials. Electrodeposited nanowires with a diameter of 60 nm and length of 7.5 μm show unusual magnetic behavior which points to the structural transformation in the temperature range of 340-395 K. Magnetic nanowires with shape memory effect offer new opportunities in various areas of research such as drug delivery or nanorobotics. Template-assisted electrochemical deposition enables the preparation of a large amount of uniform Heusler nanowires with various chemical composition and related physical properties. Acknowledgments: This research was supported by Slovak Grant Agency VEGA 1/0053/19, Slovak Grant Agency grant number APVV-16-0079.

**References:**

[1] T. Graf, C. Felser, S.S.P. Parkin, Prog. Solid State Chem., 39, 1–50 (2011). [2] J. Alam, C. Bran, et al., J. Magn. Magn. Mater., 513, 167074 (2020). [3] I. Koh, L. Josephson, Sensors, 9, 8130 (2009). [4] L. Galdun, et al., ACS Appl. Nano Mater., 1 (12), 7066–7074 (2018). [5] S. Khan, et al., J. Magn. Magn. Mater., 465, 462−470 (2018). [6] M. Sharma, et al. AIP Advances, 9, 125054 (2019). [7] L. Galdun et al., ACS Appl. Nano Mater., 3, (8), 7438-7445 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1ec077b4141b4eb7f7eae8af375ea8f5.jpg)
Figure 1, Representation of free-standing Heusler nanowires whose properties and application possibilities strongly depend on their chemical composition.

 Functional Heusler Nanowires

Materials with a giant magnetocaloric effect near ambient temperature have been a subject of intense investi-gation in the last 20 years due to their high technological potential as magnetic refrigerators or heat pumps, and as thermomagnetic regenerators for thermal energy harvesting1. HVAC (heating, ventilation and air conditioning) technologies based on the magnetocaloric effect could lead to more environmentally friendly systems, due to higher energy efficiency and the lack of greenhouse gases1. These materials are characterized by their strong spin-lattice coupling that manifests itself in first-order phase transitions (FOPT) during which the materials undergo simultaneous or closely coupled magnetic and structural transitions. These transitions may be controlled by extrinsic (temperature, magnetic field, pressure, time) and intrinsic (composition, morphology) parameters. In the referred applications, the devices require relatively high operating frequencies (of the order of 10 Hz) in order to maximize their efficiency. Such a technological requirement implies the utilized materials should complete their FOPT rapidly (for 10Hz operating frequencies, the FOPT timescale should be in the order of few milliseconds), however, unfortunately, there are relatively few studies dedicated to these materials transition kinetics2–8. From the few reports dedicated to this topic, the ones focused on the La-Fe-Si family stand out. In these, it has been shown that the shape and the interactions between particles influence the magnetic hysteresis and the time-scale of the transitions significantly4. In the Gd-Si-Ge family of materials, the Gd5Ge4 composition has been subject of relevant kinetic studies which unveiled its magnetic glass state and a kinetically arrested AFM-FM transition5. To our knowledge there is only one preliminary study for the Gd5Si2Ge2 composition, where it has been shown that the FOPT transition can last up to 300 seconds to be completed - an impressively long time considering the required operating frequencies mentioned above6. Heusler alloys such as Ni-Mn-In exhibit a giant inverse-magnetocaloric effect along their AFM-PM transition, and display typically faster transition kinetics7. Our work will thus fit in an effort to shed light on the kinetics of the FOPTs which occur in these most prominent giant magnetocaloric material families. To accomplish this, we will thoroughly study the kinetics of FOPT, encompassing the magnetic transitions (through time-dependent SQUID measurements) and the (de) coupled structural transitions time-dependencies, their electron transport kinetics as a function of temperature, magnetic field, composition and micro-structure and then attempt to theoretically model the observed phenomena. The growing surge of interest in these unusual transitions is not only due to the pursuit of application-ready materials, but also to attempt to provide answers to purely scientific questions such as how the transition kinetics of the different material families compare and how they change with different magnetovolume couplings and different morphologies (macro, micro and nanostructured). Bulk samples of the above mentioned materials families were produced and their single-phase nature, magnetic and structural properties were assessed via Scanning Electron Microscopy, SQUID magnetometry and X-ray Diffraction. As preliminary work, we have followed the time dependent magnetic field (SQUID) measurement protocol done in8 for a bulk (6x2.5x2 mm) Gd5Si2Ge2 sample. We analyze the evolution of the magnetization of the sample through time, while subjected to initially increasing and then paused fields: the fields are increased with a constant sweep rate of 70 mT/s until a given Hpause value, which is maintained for 300 seconds. Not only is magnetic hysteresis detected, but also a significant difference is observed between magnetization vs time curves obtained by two different measurement protocols: 1) a thermal “reset”, where in between measurements the sample is heated up to 45K above Tc=270K and cooled down again before the following measurement, and 2) no thermal “reset”, where the sample temperature is unchanged before subsequent measurements (see figure 1). In both, one can see once the field is stopped (at t=tpause), the rate of increase of the magnetization slows down, but keeps evolving in time. We made measurements for different temperatures a few degrees above Tc (T=283K in the presented results) so that the sample begins in its paramagnetic state and the transition to the high magnetization state must be induced by the applied field. At the given temperature, the field is increased at 70 mT/s rate until a given field value is reached (HPause) and the M(H) curves show a relaxation behavior - vertical lines in figure 2. As can be seen, the relaxation has non monotonous behaviour, increasing until a maximum at the critical field value around 2 T, and then decreasing again for higher Hpauses. The measurements followed protocol 1, where the relaxation is more significant.

**References:**

1) V. Franco, J. S. Blázquez and J. J. Ipus, Prog. Mater. Sci. Vol. 93 p. 112–232 (2018) 2) V. Basso, M. Piazzi and C. Bennati, Physica Status Solidi B Vol. 255, Issue 2 (2017) 3) A. Biswas, Y. Mudryk and A. K. Pathak, J. Appl. Phys. 126, 243902 (2019) 4) M. G. Zavareh, Y. Skourski and K. P. Skokov, Phys. Rev. Applied 8, 014037 (2017) 5) J. D. Moore, G. K. Perkins and K. Morrison, J. Phys.: Condens. Matter Vol. 20, 465212 (2008) 6) J. Leib, J. E. Snyder and T. A. Lograsso, J. Appl. Phys. 95, 6915 (2004) 7) L. Pfeuffer, T. Gottschall and T. Faske, Phys. Rev. Materials 4, 111401(R) (2020) 8). E. Lovell , A. M. Pereira and A. D. Caplin, Adv. Energy Mater. Vol. 5, Issue 6 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/33ca740aa8e7cb74167544f6139bf403.jpg)
The evolution of the magnetization for a measurement with protocol 1) (M(t) - thermal "reset") and another with protocol 2) (M(t) - no "reset") and the applied field H(t) increasing at 70mT/s and pausing at Hpause=2.2 T.

![](https://assets.underline.io/uploads/markdown_image/1/image/f853dc79d741d8ca99e0daab54dcdaf2.jpg)
The M vs H curves for different maximum paused fields, Hpause. In the inset, the M vs T curves (for constant field of 0.1 T) are shown. The vertical bar at 283K highlights the temperature at which the M vs H curves were obtained.

 Kinetics of First-Order Phase Transitions in Magnetocaloric Materials

The use of a significant share of consumed energy is dedicated to refrigeration and heating systems. Hence, innovating the current state of refrigeration and heating systems to improve their efficiencies is a critical challenge to be tackled, especially under the quest of global warming mitigation. Magnetocaloric (MC) systems are one of the most promising innovations, as their theoretical coefficient of performance (COP) is significantly larger than that of vapor-compression systems. MC systems rely on the reversible magnetocaloric effect where applying (or removing) magnetic fields (H) changes the thermodynamic state of the material in such a way that, in adiabatic processes, the temperature increases (or decreases) [1]. Although the development of magnetocaloric systems is now in a relatively mature phase, the geometrical and operating optimization is still a time consuming task. One way of optimizing a system is by predicting what are the performance values if using a set of geometrical and operating parameters. In that respect, the recent interest of artificial intelligence lead to the development of several statistical learning techniques and respective algorithm implementations [2]. These techniques have recently been used in a wide number of reserarch fields. One specific class of statistical techniques concerns supervised learning, where regressors (or classifiers) are trained based on datasets with continuous (or bolean) output values [2]. In this work, different statistical learning regressors are applied, and critically compared, in predicting the three main performance values for a generic magnetocaloric heat pump: no load temperature span, heating power and COP [4]. Four different regressors were used: ordinary least squares (ols), ridge, lasso, and K-nearest neighbors (KNN). The used dataset was obtained with the recently developed heatrapy framework to compute caloric systems [5]. The minimum average relative error of the temperature span, heating power and COP were 23%, 29% and 31%, respectively, as can be seen in Fig. 1. The Lasso regressor shows the best performance with the order of the polynomials. The best order of polynomials range between 3, for the heating power, to 5, for the COP. The worse performance in predicting the three performance values occurs when using the KNN regressor. Furthermore, the application of regressors to the dataset is more adequate to evaluate the temperature span rather than energetic performance values.

**References:**

[1] A. Kitanovski et al., Magnetocaloric Energy Conversion. Springer (2015). [2] C. M. Bishop, Pattern recognition and machine learning. Springer (2006). [3] C. Aprea et al., Int. J. Refrig. 82 (2017) 238. [4] D. J. Silva et al., Energy and AI, 2 (2020) 100030. [5] D. J. Silva et al., SoftwareX 7 (2018) 373.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4552fbdd65b2086aba0ca2c6a67e6fc9.jpg)
Figure 1: Minimum average relative error of the temperature span, heating power and COP for the different used regressors.

 Predicting the performance of magnetocaloric heat pumps using statistical learning algorithms

Magnetic refrigeration, which is a way to cool a matter with a magnetic field, was discovered more than 100 years ago. For the last several decades, the magnetic refrigeration has been intensively studied for possible application of refrigeration near room temperature. More recently, the magnetic refrigeration research field was also opened for low target temperature for the purpose of hydrogen liquefaction with condensation temperature of 20 Kelvin. However, in most of the studies, high magnetic fields, which is not lower than several Tesla, were necessarily used to obtain a large entropy change, leading to large energy costs to operate a superconducting magnet. Alternatively, we here propose high efficient cooling technique where small magnetic field changes superimposed on a static bias magnetic field can obtain one order magnitude higher cooling efficiency than the typical magnetocaloric materials. In the case of Ho, the cooling efficiency reaches ΔSM/Δμ0H = −31 J kg−1K−1T−1. The temperature range with high efficiency can be adjusted by varying the bias magnetic field. We hope that the presently provided small field controlled magnetic refrigeration technique will be a standard method, equipped with permanent magnets, for hydrogen liquefaction as an alternative to conventional gas compression-based cooling.

**References:**



**Images:**

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