Magnetocaloric Materials for Hydrogen Liquefaction

 Magnetocaloric materials for hydrogen liquefaction CarlosRomero-Muñiz,1,* Jia YanLaw,1 JorgeRevuelta-Losada,1 Luis M.Moreno-Ramírez,1 and VictorinoFranco1,* *Correspondence: [email protected]（C.R.-M）; [email protected] (V.F.) Received: May 16, 2023; Accepted: June 21, 2023; Published Online: December 6, 2023; https://doi.org/10.59717/j.xinn-mater.2023.100045 ©2023 The Author(s). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). GRAPHICAL ABSTRACT PUBLIC SUMMARY ■Magnetic refrigeration is a key enabling technology for hydrogen as an energy vector. ■Adequate material selection is crucial for this application. ■A critical review of over 400 magnetocaloric compounds is provided. Materials REVIEW The Innovation Materials 1(3): 100045, December 13, 2023 1  Magnetocaloric materials for hydrogen liquefaction CarlosRomero-Muñiz,1,* Jia YanLaw,1 JorgeRevuelta-Losada,1 Luis M.Moreno-Ramírez,1 and VictorinoFranco1,*  1Departamento de Física de la Materia Condensada, ICMS-CSIC, Universidad de Sevilla, P.O. Box 1065, 41080-Sevilla, Spain *Correspondence: [email protected]（C.R.-M）; [email protected] (V.F.) Received: May 16, 2023; Accepted: June 21, 2023; Published Online: December 6, 2023; https://doi.org/10.59717/j.xinn-mater.2023.100045 ©2023 The Author(s). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Citation: Romero-Muñiz C., Law J.Y., Revuelta-Losada J., et al., (2023). Magnetocaloric materials for hydrogen liquefaction. The Innovation Materials 1(3), 100045.  The expected energy transition to hydrogen gas as a greener energy vector has revived the interest in magnetic refrigeration at the cryogenic range, specifically between 20 and 80 K, with the vision to develop a new generation of hydrogen gas liquefiers. From the materials science point of view, the search for magnetocaloric materials containing mainly non-critical elements with a significant response in that temperature range, together with good cyclability and stability, is a challenging task. Given the increasing interest of the research community on this topic, we aim to establish a comprehensive catalog of the magnetocaloric compounds characterized so far, to be used as a starting point for further research. For this purpose, a systematic outlook of the state of the art is presented here, with the analysis and classification of more than 400 cryogenic magnetocaloric materials, divided into five large families according to their physicochemical properties. Moreover, we provide detailed information about their magnetocaloric properties, magnetic behavior, and transition characteristics together with criticality, which will facilitate the future search for optimal compounds.  INTRODUCTION The current global energy landscape is highly dependent on carbon-based fuels, which have a significant impact on global warming that is already affecting our way of life. This motivates a pressing need to replace our actual energy carriers. For that purpose, the most promising green and clean option is hydrogen gas, and its use is expected to exponentially increase in the years to come.1-3 Liquefying the gas is a crucial step in the final adoption of hydrogen as an energy vector because of its efficient transportation and storage.1,2 This will require liquefaction systems to increase energy efficiency, reduce losses, enhance safety, and enable up-scaling; these requirements, up to the moment, are not completely fulfilled by conventional systems based on Joule- Thomson expansion. To overcome these challenges, refrigeration based on the magnetocaloric effect (MCE) offers the possibility of an alternative and green technology.3-5 The MCE is defined as the reversible temperature/entropy change produced in a magnetic material subjected to magnetic field variations in adiabatic/isothermal conditions. Since its discovery by P. Weiss and A. Picard in 1917 in nickel at 630 K and its subsequent physical description in 1921 by P. Weiss,6,7 the capability of the MCE was rapidly exploited. The first breakthrough was in 1933 when W. F. Giauque and D. P. MacDougall8 reached temperatures below 1 K, using Gd2(SO4)3·8H2O, a paramagnetic gadolinium salt, that shows a strong temperature dependence of the magnetization with a large MCE close to zero kelvin. Since those early stages, the possibility of taking advantage of the MCE in every temperature range, depending on the working material, was evidenced, with a larger relevance in the vicinity of magnetic phase transitions where usually the magnetocaloric response is maximized. While paramagnetic salts offer the possibility of achieving ultralow temperatures, it is shown that the use of materials with near-room temperature phase transitions could be used for refrigerators.9 A paradigmatic example is elemental gadolinium, a ferromagnet with a Curie temperature of 292 K. The research focused on near-room temperature magnetic refrigeration was drastically enhanced at the end of the 20th century by the discovery of materials with an extremely large (or giant) MCE response,10-15 promoting the fabrication of many working prototypes of refrigerators all over the world.5 Nowadays, hundreds of magnetocaloric materials have been fully characterized, with transition temperatures ranging from one to several hundred kelvin. These include alloys, intermetallic compounds, oxides, ceramics, molecular solids, etc..16-20 More recently, an intermediate temperature range between 10 and 80 K is progressively gaining much attention due to its potential applications for gas liquefaction and storage. Given that liquid nitrogen can be produced below 77 K using conventional techniques based on the Hampson-Linde cycle, the challenge arises when trying to obtain other gases of lower boiling points, like hydrogen, in large quantities. Molecular hydrogen has a boiling point of 20.3 K and is one of the very few gases —along with helium and neon —that heats up during thermal expansion, which is a significant drawback for current industrial technology.21 Both the cryogenic (below 120 K) and conventional (above 120 K) magnetic refrigeration technologies are considered as energy-efficient alternatives to conventional devices based on mechanical compressors (with an efficiency increase of 50 %22).3-5 The core of these setups is a magnetocaloric material that acts as the working material and is controlled by the application and removal of magnetic field, which is typically generated by permanent or superconducting magnets. In general, the system absorbs heat from a cold load and releases it to the hot reservoir following a standard thermodynamic cycle, such as the ideal Carnot type illustrated in Figure 1, where the intensive variable is magnetic field instead of pressure. The heat transfer between the working material and the reservoirs occurs through a transfer medium made of gas, liquid or the magnetocaloric material itself. The idea of using magnetic refrigeration to produce liquid hydrogen dates to the 1990s, when the first prototypes appeared.23 Typically, they are designed to use helium as a heat transfer fluid and precooled liquid nitrogen as an input to the hot reservoir. Since compression-based refrigeration has very low efficiencies at cryogenic temperatures (usually less than 20 % of the ideal Carnot efficiency),24 magnetic refrigeration has been established as a promising alternative to fulfill this industrial requirement. For this purpose, several working prototypes have been built to date.25-31 The most competitive ones are those based on two-stage active magnetic refrigeration schemes and have already demonstrated good performance.26,27 Moreover, the use of superconducting magnets is feasible given the operating temperature range of these devices. Thus, devices can operate under high magnetic fields of several tesla. Even so, this technology is still at an early stage of development and if it is to become a fully competitive option for the production of liquid hydrogen, the appropriate selection of magnetocaloric materials must be addressed. The present review article aims to provide a comprehensive reference on magnetocaloric materials suitable for hydrogen liquefaction. Magnetocaloric working materials can be classified into those undergoing first (FOPT) or second order phase transitions (SOPT). Depending on the application, the magnetic transition should be optimized by modifying its  Entropy T (K) 20 80 Liquid H2Vapor H2 Magnetocaloric Carnot Cycle Heat outHeat in Figure1.An ideal magnetocaloric Carnot cycle operating between the temperatures of liquid nitrogen (hot reservoir) and liquid hydrogen (cold reservoir)This thermodynamic cycle, and many others, is capable of producing liquid hydrogen starting from liquid nitrogen temperatures. REVIEW 2 The Innovation Materials 1(3): 100045, December 13, 2023 www.the-innovation.org/materials order or tuning the response towards the desired temperature range. Typically, FOPT responses are larger in magnitude but, at the same time, they usually display thermal hysteresis that hinders the cyclability of the material and seriously affects its performance in devices.32 For cryogenic applications in the range of 20-80 K, the highest magnetocaloric responses are found in rare-earth (RE) based materials due to their typically low transition temperatures and large magnetic moment.26,27,29,33 However, the criticality of some elements might prevent its large-scale applications. The reduction of RE elements as well as other critical elements without reducing magnetocaloric response will push forward the industrial implementation of this technology. This review paper analyzes more than 400 cryogenic magnetocaloric materials suitable for hydrogen liquefaction, paying special attention to composition, magnetocaloric properties, and magnetic phase transition. They are grouped into five different groups or families according to their physicochemical properties, as illustrated in Figure 2. This includes (1) binary and pseudobinary intermetallics; (2) ternary intermetallics with main group elements; (3) borides, nitrides, carbides and chalcogenide compounds (labeled as rare-earth non-metals in the figure); (4) rare-earth oxides; and (5) rare-earth amorphous / high-entropy alloys (HEA). Additionally, open topics pertinent to the material families and their performance are included in this compelling, and critically reviewed, compound materials catalog for gas liquefaction. This is complementary to recent reviews focused on specific families of magnetocaloric materials for cryogenics34-40 and to a perspective paper on the current trends of magnetocaloric materials.41  BRIEF SURVEY ON MAGNETOCALORIC EFFECT CHARACTERIZATION ΔSiso ΔTad ΔSiso ΔTad ΔSiso The MCE is quantified by two complementary magnitudes: the isothermal entropy change ( ) and the adiabatic temperature change ( ) driven by a varying magnetic field H . Both and can be measured directly or calculated indirectly through other measured magnitudes, with the indirect calculation of being the most extended in the literature by employing the Maxwell relation:  ΔSiso (T,ΔH) = μ0 H w 0( ∂ M ∂ T)H′ dH′ ,(1) μ0 ΔTad where is the magnetic permeability of vacuum. Similarly, for :  ΔTad (T,ΔH) = T(exp(−μ0 H w 0 1 cH( ∂ M ∂ T)H′ dH′)−1),(2) c ΔTad ≪T ΔTad where is the specific heat. Near the phase transition, if and the specific heat ( c ) is field independent, can be approximated to ΔTad (T,ΔH)≈ − TΔSiso (T,ΔH) c(T),(3) ΔTad although it is based on strong approximations (specially for first-order transitions) and its proper use is not trivial.42 It has been shown that by employing an effective specific heat in martensitic transformation, it is possible to properly use it for first-order materials.43 To indirectly obtain , it is much more reliable to calculate it through the total entropy curves obtained from specific heat measurements at different fields: S(T,H) = T w 0k T′ c(T′ ,H)dT′ ,(4) ΔTad where the entropy at zero kelvin is neglected. Next, is obtained as ΔTad (S,ΔH) = T(S,H)−T(S,0),(5) S(T,H) T(S,H) ΔSiso where is inverted to . Similarly, can also be obtained from specific heat measurements as: ΔSiso (T,ΔH) = S(T,H)−S(T,0).(6) ΔSiso ΔTad RC Thot Tcold Other magnitudes derived from and are routinely used to evaluate materials’ performance, like the refrigerant capacity ( ), which accounts for the heat that can be exchanged between the hot and cold thermal reservoirs (at temperatures and , respectively).44 It is calculated as  RC = Tcold w Thot |ΔSiso (T’,ΔH)|dT’.(7) The reservoir temperatures depend on the refrigerator design, but they are usually approximated by the limits of the full width at half maximum Materials  20.7% 21.7% 22.9% 22.5% 12.1% Binary Intermetallics Ternary Intermetallics RE Non-Metal Compounds RE Oxides RE Amorphous & HEA Gas Liquefaction Magnetocaloric Material Families 6.5 2.4 5 2.3 4 0.3 6.0 2.0 3.0 4.0 5.0 1.0 36.2 30.6 56.0 42.4 18.4 5 T ∆Siso (J kg-1 K-1) Transition temperature range (K) Criticality range 135 150 87 67 97 Figure2.Classification of the cryogenic magnetocaloric materials analyzed in this reviewFor each family of material, with its corresponding importance in the scientific literature, the maximum magnetocaloric response, the temperature range where these materials have a significant response, and the criticality range are shown. The calculation of criticality is explained in the last section of this review. REVIEW The Innovation Materials 1(3): 100045, December 13, 2023 3 ΔTFWHM ΔSiso ( ) in the curve. Thus, RC can be estimated by the product:  RCP =|ΔSmax iso | · ΔTFWHM,(8) RCP ΔTFWHM which is known as the relative cooling power ( ). The value should be considered with caution because it tends to overestimate the actual temperature span in materials with small magnetocaloric responses. It should be mentioned that more precise magnitudes or parameters have been developed. For instance, the Temperature Averaged Entropy Change ( TEC ),45 corrects for deceptively large RC responses caused by shallow maxima. However, this magnitude is less discussed in the literature and, unfortunately, cannot be used for a general comparison. Similarly, the coefficient of performance ( COP ) offers a more precise tool than RC and RCP for evaluating the energy conversion of the materials as it also accounts for magnetization hysteresis during working conditions and allows comparison among different cooling technologies.46 However, this magnitude is also scarcely reported in publications. A recent overview of magnetocaloric measurement techniques, together with their application to the study of phase transitions, is presented in ref.47  BINARY INTERMETALLIC COMPOUNDS Binary compounds between a RE element and a metal, such as transition metal (Fe, Co, Ni, Mn, Cu, Ag, Rh, Pd, etc.), p-block metal (Al, Ga or In) or even a metalloid (Ge or Si) are included in this first group. These compounds can be found in a wide range of stoichiometric combinations, the most prevalent of which are RM, RM2, R3M, R3M2, RM5, etc. Even uncommon stoichiometries, such as R5M4, R3M7 or R7M12, have a significant impact in this field and their basic magnetic properties have been reported in the last quarter of the previous century.48 The most relevant compounds with potential applications in cryogenic magnetic refrigeration will be discussed in the following. Equiatomic compounds with generic formula RM have been extensively studied40 and some of them display remarkable MCE. The most studied families are RZn, RNi and RGa. ΔSiso RZn compounds with CsCl-type crystal structure undergo a ferromagnetic to paramagnetic SOPT at 267, 204, 102, 73, 17 and 8.4 K for R = Gd, Tb, Dy, Ho, Er and Tm respectively.49-52 In addition, a spin reorientation (SR) transition is observed in some of them (R = Tb, Ho and Tm). In particular, HoZn has very broad curves due to two phase transitions, leading to a remarkable refrigerant capacity.51 |ΔSiso| ΔSiso RNi compounds have ferromagnetic behavior with possible low-tempera- ture SR phase transitions at around 10 K. Non-collinear magnetism is observed in all compounds except for GdNi, which is a simple ferromagnet. They crystallize in FeB- or CrB-type crystal structures and their Curie temperatures vary between 8 and 71 K, being GdNi the one with the largest Curie temperature.53 Thus, the whole series has potential applications for hydrogen liquefaction. Most of them have been characterized for their MCE54-58 except for the cases of NdNi and TmNi. Overall, from R = Gd to Er they present large values of between 15 and 30 J kg−1K−1 for an applied field of 5 T. All of them also exhibit large values of RC , especially HoNi. This is due to the coexistence of two phase transitions that leads to a table-like MCE over a broad temperature range. Despite having an intermediate value of of 14.5 J kg−1 K−1, the RCP value is estimated to be 780 J kg−1 for an applied field of 5 T.56 Zheng et al.59 have studied the pseudobinary HoxEr1-xNi system for the whole range of x, producing samples with Curie temperatures between 11 and 36 K. The refrigerant capacity increases with increasing Ho content due to the table-like MCE of HoNi. |ΔSiso| RGa gallides crystallize with the CrB-type structure and their magnetic properties are rather singular. Except for PrGa and TmGa,60-62 which display a distinctive behavior including both ferromagnetic and antiferromagnetic ordering, all the rest of the RGa compounds undergo two phase transitions leading to a remarkable MCE.62-67 One transition is associated with a ferromagnetic ordering, which can be either FOPT or SOPT, and the second is due to a SR transition. The former covers the range of 30-180 K with a decreasing trend from Gd to Er, while the latter always occurs at lower temperatures within the 15-40 K range. They present large values of , with TmGa ΔSiso being the one with the largest magnitude. Interestingly, HoGas exhibit two phase transitions occurring at 20 and 69 K, leading to a table-like MCE with a large refrigerant capacity.62,66 Moreover, the use of solid solutions combining two rare-earth elements is especially suitable for expanding magnetic refrigeration even further in these compounds. For instance, Tm1−xHoxGa can be synthesized for all values of x,62 leading to intermediate compounds exhibiting three phase transitions occurring within a relatively small temperature range. This is because they merge the spin reorientation transition of HoGa with the two successive phase transitions observed in TmGa. Another interesting strategy is to alloy Gd and Er.68 Since the transition temperatures for GdGa are much higher than those of ErGa, in the GdxEr1-xGa system the peaks can be easily tuned by increasing the content of Gd, achieving compounds with extraordinary refrigerant capacity, as shown in Figure 3A. |ΔSiso| Other examples of equiatomic binary compounds mainly crystallize in CsCl structure, such as TmCu, TmAg (both with very poor MCE),72 GdCd0.8Ru0.2,73 GdRh (both with better MCE responses),74 NdSi,75 NdPd,76 ErAl77 and HoAl77 crystallize within orthorhombic DyAl-type structure, where the latter displays successive AFM to FM to PM transitions at 13 and 20 K, leading to remarkable values of 22.5 J kg−1 K−1 for 5 T. |ΔSiso| The MCE of R2In ferromagnetic compounds reveals a few promising candidates for hydrogen liquefaction. Tb2In, Dy2In, Ho2In and Er2In crystallize in a Ni2In-type crystal structure and exhibit Curie temperatures of 165, 130, 82 and 42 K respectively. They possess remarkable MCE [78–81], especially Ho2In, whose additional SR transition at 32 K on top of the FM to PM transition leads to a large table-like MCE that expands over a broad temperature range.78 Surprisingly, Eu2In crystallizes in a different type of crystal structure (Co2Si-type), exhibits FOPT without apparent hysteresis, and its MCE magnitudes are the largest among the R2In series, with a maximum of 33 J kg−1 K−1 at 55 K for an applied field of 5 T (see Figure 3B).69 |ΔSiso| ΔTad ΔSiso ΔTad Many RM2 compounds are known to crystallize within the cubic MgCu2- type crystal structure, or alternatively, the other two so-called Laves phases (i.e., hexagonal MgZn2 or cubic MgNi2). Over the last few years, their magnetic properties have been extensively studied, . Many of them, especially the RNi2, RCo2 and RAl2 series, have been fully characterized for their MCE. RCo2 compounds could undergo a FOPT with a large MCE associated to it where among them only HoCo2 and ErCo2 show transition temperatures below 80 K (78 and 32 K respectively).82,83 Both compounds display very large values of and : 20 J kg−1 K−1 and 8.5 K for HoCo284 and 32 J kg−1 K−1 and 7.2 K for ErCo285,86 for an applied field of 5 T. Interestingly, the transition temperature can be finely tuned by alloying two different rare-earth elements87 or shifted towards lower values after the partial substitution of Co by Ni84,88 or other elements, as shown in Figure 3C. Solid solutions of RAl2 compounds have been regarded as potential candidates for low temperature refrigeration since the early days of magnetocaloric research.89,90 This is because most of these compounds display FM to PM SOPTs between 13 and 80 K with a remarkable MCE.91 In particular, those compounds with R = Dy, Ho and Er show an additional SR transition below the Curie temperature which enhances their MCE response,92,93 reaching the outstanding mark of 36.2 J kg−1 K−1 and 11 K for and respectively for ErAl2.92 Very recently, Liu et al.94 have explored the MCE of NdAl2 and PrAl2 together with some of their rare-earth solid solutions leading to remarkable figures. A rather similar behavior but with a lower MCE magnitude has been observed for the RNi2 series, which has been investigated in depth.95-100 For this reason, combinations of RM2 Laves phases are regarded as strong candidates for hydrogen liquefaction applications and, indeed, are the preferential choice when building operating prototypes.26,27,29,31 However, it is important to note that, although the RM2 series with M = Ni, Co and Al has attracted most of the attention in the materials community,70,101 there are still other combinations that have received less attention despite having promising properties. This is the case with the RMn2 series102 or others that have not even been explored yet, like RMg2. Moreover, it is important to remark that not all RM2 compounds are Laves phases, like the case of RCu2 compounds, which adopt an orthorhombic CeCu2-type crystal structure, leading to very interesting magnetic properties.103-105 R3Co might be regarded as another promising family of compounds. They are mainly constituted by rare earth elements, which carry the magnetic moment, while Co acts as nonmagnetic element and, at the same time, stabi- REVIEW 4 The Innovation Materials 1(3): 100045, December 13, 2023 www.the-innovation.org/materials ΔSiso |ΔSiso| lizes the AF ordering. They crystallize in Fe3C-type crystal structure and present complex magnetic behavior with transition temperatures between ~5 K (Tm3Co)106 and ~130 K (Gd3Co).107 Er3Co, with arguably the best MCE response among the series, shows a very complex non-collinear magnetism and does not follow the general trend observed in the series.108,109 Most of the other compounds present two close successive phase transitions due to the presence of two types of magnetic orderings. The Tb3Co,110 Dy3Co111 and Ho3Co112 compounds present transition temperatures that fall within the appropriate range between 20 and 80 K, with two peaks or a table-like character observed in their curves, which all give rise to high RC values. The transition temperatures of this class of compounds can be easily tuned by either incorporating a new transition metal or rare-earth elements by means of solid solutions. For instance, the Curie temperature of Gd3Co can be lowered after Ru incorporation in the Gd3CoxRu1-x.113,114 Alternatively, the solid solution between Er and Gd allows a great tunability of the transition temperature in Er3-xGdxCo.115 There are more compounds with R3M stoichiometry and most of them have not been systematically studied for magnetocaloric applications. Even so, there are a few promising examples like Gd3Ru, whose Curie temperature is 54 K and displays a remarkable MCE with values up to 30 J kg−1 K−1 for 5 T.116 Again, the solid solution between Gd and Er can be used to adjust the Curie temperature with remarkable precision.117 Gd3Rh and Tb3Rh also show good magnetocaloric properties but with transition temperatures above 100 K.118,119 In addition, Ho3Ru and Ho3Rh have been investigated120 in samples that contain other secondary phases that also contribute to the global MCE but with moderate performance. R3M2 intermetallic compounds with Er3Ni2-type crystal structure are not so common and their MCE performance has not been studied systematically so far. R3Ni2 compounds with R = Er and Ho behave as ferromagnets with an additional SR transition at low temperatures.121 The broad R3NiCo series, with solid solution of transition metals, have been analyzed by Herrero et al.122 They present essentially the same features of R3Ni2 compounds, same crystal structure and magnetic behavior without a clear SR transition. The Curie temperature monotonically decreases with increasing atomic number through the lanthanide series, from 97 to 7 K, following an almost exact geometric progression with 1/2 of common ratio. RC is quite large in these compounds, reaching up to 516 J kg−1 for Tb3NiCo. Similar features are observed in Er3Rh2 and Ho3Rh2 (despite having a different Y3Rh2-type crystal structure), while Nd3Rh2 orders antiferromagnetically and shows poorer MCE performance.123 Another compound with this stoichiometry but with a distinctive tetragonal Zr3Al2-type crystal structure is Ho3Al2, which displays a spin reorientation transition at 31 K followed by a FM to PM phase transition at 40 K, leading to a remarkable RC value of 704 J kg−1 for an applied field of 5 T.124 The series of RNi5 is an interesting group of compounds due to its low content in rare-earth elements.125 They behave as simple ferromagnets with transition temperatures between 10 and 30 K, except PrNi5 which is a param- Materials  Eu-II Eu-I Eu-I Eu-II Eu-II a b c A B C D -∆Siso (J kg-1 K-1) -∆Siso (J kg-1 K-1) -∆Sm (J cm-3 K-1) ∆Tad (K) T (K)T (K) 20 15 10 5 0 0 0 0 2 4 6 0.1 0.2 0.3 0.4 50 100 150 200 90 80 70 60 50 40 30 0 8 16 24 32 40 GdxEr1-xGa 5 T x = 0 0.1 0.2 0.3 0.4 0.6 0.8 1 1 T 2 T 5 T 7 T T (K) T (K) 0 20 40 60 80 100 0 20 40 60 80 100 Tb H2Tb N2 ErCo1.8Ni0.17Al0.03 HoCo1.8Ni0.15Al0.05 HoCo1.9Ni0.06Fe0.04 ErCo1.96Fe0.04 ErCo1.8Ni0.17Al0.03 HoCo1.77Ni0.2Al0.03 HoCo1.8Ni0.15Al0.05 HoCo1.9Ni0.06Fe0.04 ErCo1.85Ni0.11Fe0.04 ErCo1.9Ni0.06Fe0.04 ErCo1.96Fe0.04 ΔSiso ΔSiso ΔSiso ΔTad Figure3.Magnetocaloric response for some promising binary intermetallic materials as well as some examples of representative crystal structures(A) for 5 T for GdxEr1-xGa solid solutions (reproduced with permission of AIP),68 (B) for 7 T for Eu2In together with its cell,69 (C) and for 5 T (upper and lower panel, respectively) for several RM2 phases70 and (D) crystal structures of orthorhombic α- (left) and monoclinic β-Gd5(Si2Ge2) (right) (reproduced with permission of APS).71 REVIEW The Innovation Materials 1(3): 100045, December 13, 2023 5 ΔTad agnetic compound with inverse MCE. Among them, TbNi5 and GdNi5 seem more suitable for hydrogen liquefaction, with transition temperatures of 23 K and 32 K respectively125,126 and remarkable . A very interesting feature of RNi5 compounds is the possibility to produce ternary compounds of the type RNi4M or RNi4X with the incorporation of other metals or nonmagnetic main group elements, which has not yet been systematically studied. For instance, TbNi5 shifts its transition temperature to larger values after partial replacement of Ni by Co or Fe, although its MCE worsens.126 Conversely, GdNi4Al and GdNi4Si display even better MCE than the parent GdNi5 but have slightly lower Curie temperatures.127 ΔSiso ΔSiso The R5(SixGe1-x)4 pseudobinary alloys have attracted extraordinary attention since the discovery of giant MCE in Gd5Si2Ge2 in 1997.10 From that breakthrough, intense research has focused on this system revealing an extreme complex interplay between their magnetic and crystallographic properties.71,128-130 In brief, R5Si4 and R5Ge4 compounds usually crystallize in orthorhombic crystal structures of either Gd5Si4- or Sm5Ge4-type. However, for intermediate values of x~2, there is a monoclinic phase where the giant MCE could be observed. The FOPT is accompanied by a structural transformation that is responsible for the unexpected large magnetothermal response. The trends in magnetic ordering and transition temperature are difficult to rationalize, but the striking difference in transition temperature between the germanide and silicide counterparts can be attributed primarily to the formation of a different number of covalent bonds between the constituent slabs of the crystal structure in each phase (see Figure 3D). This fact was explained in the case of the Gd based alloy,71 whose transition temperature gradually drops from 336 K for Gd5Si4 to 32 K for Gd5Ge4, with all the intermediate values for increasing Ge content. Analogous compounds containing Nd, Tb, Dy and Er have been studied in detail. Nd5Si4 and Nd5Ge4 display transition temperatures at 71 and 55 K respectively, but with moderate MCE responses.131 Moreover, it seems that a giant MCE is not observed in the whole Nd5(SixGe1-x)4.131 Tb5(SixGe1-x)4 also shows remarkable MCE, but at temperatures above 100 K for the whole x range.132 Dy5(SixGe1-x)4 is a particularly interesting system as its phase transitions expand over a temperature range from 130 K (Dy5Si4) to 35 K (Dy5Ge4), but its largest MCE is observed for Dy5Si3Ge at 65 K, with a larger than 30 J kg−1 K−1.133 In the case of Er5(SixGe1-x)4, the phase transitions take place between 14 and 30 K, showing a good yet moderate MCE.134 Other remarkable compounds include Gd5Rh474 and especially Gd5Sn4,135 with an excellent MCE response. However, it should be noted that pseudobinary R5M4 phases display FOPT, usually with large thermal hysteresis. This means that its use in devices is difficult to implement due to the mechanical degradation of the materials upon operational cyclic conditions and because they usually show poor refrigerant capacities due to the sharp shape of the peaks, despite their large magnitude. The occupied f-orbitals of lanthanides allow the formation of intermetallic compounds with unusually large stoichiometric coefficients. One example of such type of compounds relevant to magnetocaloric applications is the R12Co7 series. They crystallize following a complicated Ho12Co7-type monoclinic crystal structure containing four different types of coordination polyhedra for the RE sites in the unit cell. The compounds containing Gd, Tb and Dy undergo only one ferromagnetic FM to PM transition at temperatures of 163, 100 and 64 K, respectively.136-138 Conversely, the compounds with Ho and Er display a more complex behavior, with multiple phase transitions at lower temperatures.139,140 The possibility of using RE solid solutions to tune the MCE of these compounds had already been demonstrated in Gd12-xTbxCo141 and Er12-xHoxCo7140 systems, the latter being very promising for hydrogen liquefaction. There are a few compounds of the R5Pd2 type that have been investigated and they show moderate MCE.142-144 Related compounds in the form of R7Pd3, such as Pr7Pd3145 and Nd7Pd3,146 have also been considered as possible magnetocaloric materials. However, the high content of rare-earth in combination with Pd, an extremely expensive metal, suggests that such compounds are less economical for industrial applications, not even those with remarkable MCE like Nd7Pd3.  TERNARY INTERMETALLICS WITH MAIN GROUP ELEMENTS In this second family of rare-earth compounds, we include those ternary combinations of a lanthanide element, a transition metal and a main group element in addition to Cd or Zn that can be considered in this group.147 Note that the combinations including non-metal elements of the second period, such as B, C, N or S, will be covered separately in the next section. Similar to binary rare earth compounds, the number of possible combinations in this second family is large. The most common stoichiometries for rare earth ternary compounds are RMX and R2M2X. The RMX compounds usually crystallize in a hexagonal ZrNiAl-type crystal structure though other structures could also exist.148 Their magnetocaloric properties have been investigated in many cases.37 On the other hand, the magnetocaloric R2M2X compounds mainly belong to tetragonal Mo2FeB2-type or W2CoB2-type crystal structures, along with some other less common structures. Many of these materials are known to display a remarkable MCE.38 In addition to these most common ones, there are many other stoichiometric possibilities that we will mention throughout this section. For clarity, the discussion thereafter in this section will focus on the various main group elements rather than the different stoichiometry. There are a few relevant cadmium, indium, or magnesium compounds among the ternary rare earth compounds with pertinent magnetocaloric properties, but the majority reported are aluminides, gallides, and silicides. |ΔSiso| Aluminides represent a large group of this type of compounds whose magnetocaloric properties have been extensively studied. Magnetic equiatomic compounds, such as ferromagnetic elements (i.e., RNiAl,149,150 RCoAl151 and RFeAl152 series) display good magnetocaloric properties. Those that contain Co and Fe behave as standard ferromagnets whereas those with Ni show antiferromagnetic ordering. The overall MCE performance follows the Co < Ni < Fe trend with transition temperatures in the range 10 - 100 K. Their transition temperatures decrease with increasing atomic mass along the Gd-Er series. Surprisingly, compound series with non-magnetic atoms, such as Cu or Ag, are also promising materials in terms of MCE. If we focus on the RCuAl series, we will find ferromagnetic compounds with Curie temperatures between 81 K for R = Gd to 2.8 K for R = Tm with remarkable values of around 10 - 17 J kg−1 K−1 and 20 - 30 J kg−1 K−1 for applied fields of 2 and 5 T, respectively.153-157 A similar behavior is observed in the RAgAl series but with lower MCE.158,159 The remaining interesting aluminides for cryogenic magnetocaloric refrigeration are further combinations of Al with Ni or Co. The series R2Co2Al164,165 and R2Ni2Al165 share some similar features with their equiatomic counterparts, in the sense that Ni compounds display AF behavior while Co compounds behave as ferromagnets. However, their magnetothermal responses are weaker than their RMX counterparts, despite an additional SR transition at low temperatures. Interestingly, GdNiAl2 and TbNiAl2 display remarkable MCE with exceptionally high RCP at temperatures around 30 and 20 K respectively,160 as shown in Figure 4A. Unfortunately, compounds with other lanthanides possess too low transition temperatures. In a similar manner, R3Ni6Al2 compounds166,167 show mainly ferromagnetic behavior and moderate MCE over a broad range of transition temperatures, from 105 K for Gd to 2.5 K for Er. Lastly, R2CoAl3 compounds,168 which are MgCu2-type Laves phases, show SOPTs and lower transition temperatures than their RCo2 counterparts, with a significantly weaker MCE. ΔSiso Rare-earth gallides occur in a great variety of combinations and many of them have been fully characterized, showing moderate MCE magnitudes. The MCE of R2M2Ga compounds have been reported both for M = Co and Ni.161,169,170 All of them possess W2CoB2-type crystal structure. Co compounds behave as standard ferromagnets and exhibit moderate MCE (see Figure 4B), whereas Ni compounds display AF ordering that transforms to FM in the presence of magnetic fields, resulting in a poor MCE. Other representative compounds include the RNiGa2 series171 and equiatomic ternary HoAgGa.172 No MCE characterization of any other compound of the RAgGa series has been reported so far. Compounds with less common stoichiometries, such as R2CoGa3173 or R6Co2Ga,174 have been studied. It is worth noting that despite the moderate magnetothermal response shown by rare-earth gallides, we can find some compounds with a large refrigerant capacity due to the broadness of their curves. This is the case for Gd6Co2Ga, whose Curie temperature is 78 K and its RCP value is estimated as high as 618 J kg−1 for 5 T.174 There are many indium compounds containing rare-earth metals showing moderate magnetothermal responses. Although they are characterized by a REVIEW 6 The Innovation Materials 1(3): 100045, December 13, 2023 www.the-innovation.org/materials rich variety of magnetic properties and phase transitions, none of them display a relevant MCE. Among them, we highlight the following as representative examples: RNiIn (see Figure 4C),162 R5Ni2In4175 and R2Cu2In176-178 with ZrNiAl-type, Lu5Ni2In4-type and Mo2FeB2-type crystal structures, respectively. EuM5In (M = Cu, Ag and Au) display complex disordered crystal structures and a moderate magnetothermal response.179 The MCE of the R2Ni2In series has also been studied, but their transition temperatures are too low for their use in hydrogen liquefaction.180 |ΔSiso| ΔTad |ΔSiso| A few magnesium and cadmium compounds have proven to be excellent candidates for magnetic refrigeration at low temperatures, e.g., equiatomic ternary RPtMg compounds,181 or the more competitive R4MMg,182-184 where M = Pt or Pd. Some of these compounds with Gd4RhIn-type crystal structure (i.e., Er4PdMg, Ho4PtMg or Er4PtMg) have FM to PM SOPT in the proximity of hydrogen liquefaction temperature with excellent magnetothermal response of around 6 J kg−1 K−1 and around 2 K for an applied field of 2 T. These values are often used as a good indicator for materials for cryogenic magnetic refrigeration. Isomorphous R4CoCd compounds also possess excellent MCE, comparable to magnesium compounds.185,186 In addition, the series R2Cu2Cd with Mo2FeB2-type crystal structure also shows good MCE properties,187-189 especially Ho2Cu2Cd, whose Curie temperature is 30 K and is accompanied by a SR transition at 15 K, leading to large values around 10 and 20 J kg−1 K−1 for applied fields of 2 and 5 T, respectively.189 Unfortunately for these combinations, Pt and Pd are extremely expensive, and Cd is often discouraged due to its high toxicity. ΔSiso |ΔSiso| ΔTad Silicides constitute an extensive family of interesting compounds. For instance, equiatomic ternary compounds, such as HoCoSi,190 ErFeSi163 or ErRuSi191 are well-known ferromagnets with a remarkable MCE and appropriate Curie temperatures (see the curves of ErFeSi in Figure 4D). The main group of silicides are those with the general formula RM2Si2 and ThCr2Si2-type crystal structure, with M = Mn, Cr, Ru, Fe, etc. Most of them present AF behavior with field induced AFM to FM FOPT and a moderate MCE. However, there are some notable exceptions, like ErCr2Si2,192 which is a ferromagnet with a SOPT and impressive MCE values: maximum of 24.1 and 29.7 J kg−1 K−1 and of 8.4 and 17.4 K for 2 and 5 T, respectively. Unfortunately, its Curie temperature is only 4.5 K, which is too low to be considered as a competitive candidate for hydrogen liquefaction applications. Several rare-earth silicides containing Pd have been reported, such as those with the formula RPd2Si193,194 or R2PdSi3,195,196 very complex magnetic behavior and poor MCE performance. Note that the Gd2NiSi3 compound197 shares similar features with the aforementioned Pd-containing compounds. Furthermore, while there are other compositions that contain other main group elements, none of them seem to exhibit a magnetothermal response good enough to be considered for magnetic refrigeration. For example, the study of magnetic properties of R2Ni2Sn compounds198 finds them with extremely complex magnetic behavior and poor MCE magnitude. Other main group element compounds include EuAuZn,199 EuAgZn,200 EuPtZn,200 EuAuGe,201 PrMn1.4Fe0.6Ge2,202 or EuFe2As2.203  RARE-EARTH - NON-METAL COMPOUNDS In this third group of compounds, we discuss rare earth compounds that combine lanthanides with nonmetallic main group elements. This section includes the limiting case of boron element, while those compounds containing oxygen will be discussed exclusively in the next section since oxides constitute a separate and broad group of compounds. Thus, this section focuses mainly on rare earth borides, carbides and nitrides with a few cases of sulfides. |ΔSiso| ΔTad |ΔSiso| The recent discovery of HoB2 as a promising candidate for cryogenic magnetic refrigeration204 has brought renewed attention to boron compounds. This is because HoB2 possesses one of the largest (about 40 J kg−1 K−1 for 5 T) near the boiling point of hydrogen, with a of 12 K (see Figure 5A for other values of applied field). This feature was further confirmed by J. Li, et al.,205 pointing at slightly lower values of about 35 J kg−1 K−1. Previously, the magnetocaloric properties of DyB2 had been studied, with a lower but remarkable MCE.206 DyB2 and HoB2 behave as standard ferromagnets with Curie temperatures at 50 and 15 K respectively, and additional SR transitions at 20 and 12 K. The proximity between the FM to PM and SR phase transitions in HoB2 might explain the large magnetothermal response observed in this compound. The pseudobinary system formed by the solid solution of Ho and Dy (HoxDy1-xB2) has been fully studied for the whole x range.205,207 The combination of Ho and Dy in the same compound decreases but leads to a table-like response, achieving very large RC values of over 600 J kg−1.205 The Curie temperature can be tuned within the range of 15-50 K depending on the Ho and Dy ratio. More recently, the partial substitution of B by Al has been considered,208 revealing that the MCE of original HoB2 is barely affected (including the Curie point) in HoB1.5Al0.5. Given the striking price difference between Al and B, this could be a point worth of further exploration. Regarding other members of the RB2 series, TbB2 has a too high Curie temperature, i.e., 144 K,209 while the MCE of ErB2 or TmB2 has not yet been investigated. ΔTad ΔTad |ΔSiso| Other rare-earth borides include the ternary compounds RCo2B2 or RCo3B2. The RCo2B2 series is isomorphous with the RM2Si2 silicides that has been discussed in previous section. They crystallize in ThCr2Si2-type structure and can display either ferromagnetic ordering associated to a SOPT or a metamagnetic FOPT with a field induced AFM to FM transition like GdCo2B2217 or TbCo2B2.218 As reported by L. Li, et al.217-220 they display remarkable MCE properties and transition temperatures in the target range for hydrogen liquefaction. Especially, GdCo2B2 presents large of 6.7 and 15.4 K for 2 T and 5 T, respectively, and also high RC in spite of its FOPT. On the other hand, RCo3B2 compounds with CeCo3B2-type crystal structure behave as standard ferromagnets with suitable Curie temperatures for Gd, Tb and Dy compounds. In addition, they display remarkable values even for moderate values.221-224 Rare-earth carbides containing transition metals show better overall MCE performance than equivalent borides. Among these carbides, we can highlight the RCoC, RCoC2 and R2Cr2C3 series for their excellent MCE. The RCoC Materials  10 20 30 40 50 0 5 10 15 20 25 0 0 20 40 60 80 100 120 5 T 18 12 6 0 0 16 32 48 64 80 Tm2Co 2Ga Er2Co2Ga Ho2Co2Ga Dy2Co2Ga 1 to 7 T 5 T TmNiAl2 TbNiAl2 GdNiAl2 -∆Siso (J kg-1 K-1)-∆Siso (J kg-1 K-1) T (K) T (K) T (K) A B C D 18 24 12 6 0 -∆Siso (J kg-1 K-1) HoNiIn ErNiIn DyNiln TbNiln GdNiIn 0 ErFeSi 10 20 30 40 50 60 5 10 15 20 25 1 T 2 T 3 T 4 T 5 T -∆Siso (J kg-1 K-1) T (K) ΔSiso Figure4. for some promising ternary intermetallic materials(A) RNiAl2 (R=Gd, Tb and Tm) for 5 T,160 (B) R2Co2Ga (R=Dy, Ho, Er and Tm) up to 7 T,161 (C) RNiIn (R=Gd, Tb, Dy, Ho and Er) for 5 T162 and (D) ErFeSi for fields up to 5 T from magnetization (symbols) and specific heat (lines) measurements.163 (All figures reproduced with permission of AIP).   REVIEW The Innovation Materials 1(3): 100045, December 13, 2023 7 |ΔSiso| compounds with R = Tb and Er225 and R2Cr2C3 with R = Dy, Ho and Er226,227 possess good magnetocaloric properties but their transition temperatures tend to be lower than 25 K. They could undergo either FOPT or SOPT, exhibiting both ferromagnetic and antiferromagnetic ordering depending on the rare earth element, often with a field-induced phase transition from AF to FM order. On the other hand, the whole RCoC2 series with R = Gd, Tb, Ho and Er210,228,229 behaves as ferromagnetic materials with FM to PM SOPTs. They show low Curie temperatures in the range 11-28 K and large . For instance, GdCoC2, whose Curie temperature is 15 K, shows 16 and 28 J kg−1 K−1 for 2 and 5 T, respectively,210 as shown in Figure 5B. Some compounds containing boron and carbon have also been studied for MCE, in particular, the quaternary RNiBC and RM2B2C compounds where M = Co and Ni. Those containing cobalt lead to ferromagnetic behavior and SOPTs,230 while the presence of nickel stabilizes the AFM ordering associated to FOPTs.231,232 They exhibit characteristics that seem to be more similar to those of carbides than to those of their boride analogs. Equiatomic RNiBC compounds show ferromagnetic ordering and SOPTs, at least for GdNiBC and ErNiBC,233 but their Curie temperatures are too low even for GdNiBC. |ΔSiso| ΔTad ΔSiso ΔSiso Surprisingly, with the notable exception of EuS, there has been very little research in recent years focused on the magnetocaloric properties of inorganic sulfides. It is a well-known magnetocaloric material212,234,235 behaving as a ferromagnetic semiconductor with NaCl-type crystal structure and a Curie temperature of 18 K. It displays impressive MCE figures, namely of 22 and 37 J kg−1 K−1 for 2 and 5 T, respectively, leading to RCP values of 284 and 780 J kg−1, respectively. The associated values are 7.5 and 10.4 K, respectively.212 The analogous EuSe is also a semiconductor that displays excellent MCE. However, its magnetic properties are different: it has a peculiar AF ordering after a FOPT at 4.6 K yet with very broad curves.211 The curves for 5 T of EuS and EuSe are presented in Figure 5C for comparison. Typical inorganic sulfides containing rare earth, such as NaGdS2 or LiGdS2, |ΔSiso| ΔTad may have an excellent MCE236 but their transition temperatures are below 10 K. Conversely, there are a few thiospinels with remarkable magnetic properties like CdCr2S4.237 This ferromagnetic compound has a Curie temperature of 87 K, slightly above our target temperature range, and show a of 7 J kg−1 K−1 and a of 2.6 K under an applied field of 5 T. Other related compounds like FeCr2S4 or CoCr2S4 possess much higher Curie temperatures.238 The partial replacement of Cd by Zn in CdCr2S4 shifts the Curie temperatures to lower values but, at the same time, the MCE magnitude decreases.239 Notice that spinels are a large family of materials with the general formula of AB2X4 that include oxides and other chalcogenide compounds with a unique cubic crystal structure. These compounds allow the accommodation of two different transition metals with both tetrahedral and octahedral coordination. This has led to substantial progress in the development of magnetic materials based on spinel compounds.240 In summary, further attempts are necessary to find new magnetic sulfides with transition temperatures between 10 and 80 K. We emphasize that even though many sulfides and other chalcogenides do not contain rare-earth elements, their potential as magnetocaloric compounds has not yet been thoroughly studied. |ΔSiso| Rare earth nitrides represent another promising group of compounds with distinctive properties and very good MCE features. In particular, rare earth mononitrides with the formula of RN, where R = Gd, Tb, Dy, Ho, Er, have been investigated in depth,213,214,241 along with many of their binary RE nitrides.213,215,216,242,243 All of them display NaCl-type crystal structure and a FM to PM SOPT with Curie temperatures in the region of 6 to 60 K, following the usual trend of decreasing Curie temperature along the series Gd < Tb < Dy < Ho < Er (see Figure 5D). They are dense materials in comparison with metallic materials and possess a high thermal conductivity. Rare earth nitrides are very stable from the chemical point of view and do not react with hydrogen gas, in contrast with most intermetallic compounds. For an applied field of 5 T, some of these nitrides, such as HoN or ErN, present very large  HoB2 A B C D -∆Siso (J kg-1 K-1) -∆Siso (J kg-1 K-1) ∆Tad (K) 0 0 0 10 20 30 40 50 60 2 4 6 8 10 12 10 10 10 20 30 40 5 15 15 25 25 35 35 20 20 30 30 40 T (K) T (K)T (K) 1 T 2 T 3 T 4 T 5 T -∆Siso (J kg-1 K-1) 0 0 10 20 30 40 50 60 70 10 20 30 40 T (K) 5 T EuS EuSe 0 20 40 60 80 100 -∆Siso (J kg-1 K-1) 0 10 20 30 40 T (K) 5 T GdN TbN DyN ErN HoN GdCoC2 0-1 T 0-2 T 0-3 T 0-4 T 0-5 T 0-6 T 0-7 T 5 T 4 T 3 T 2 T 1 T ΔSiso ΔTad ΔSiso ΔSiso ΔSiso Figure5.Magnetocaloric response for some promising non-metallic materials(A) Both and (left and right panel, respectively) of HoB2,204 (B) of GdCoC2,210 (C) of EuS and EuSe (data from refs.211,212) and (D) of RN (with R=Gd, Tb, Dy, Ho and Er) after data from refs.213-216 REVIEW 8 The Innovation Materials 1(3): 100045, December 13, 2023 www.the-innovation.org/materials ΔTad over 30 J K−1 kg−1 and around 10 K,244 whose combined values make them emerge as the magnetocaloric materials with the best performance in the target temperature range (see Figure 5D). More recently, they have been synthesized as nanoparticles which leads to remarkable magnetocaloric properties.245,246  RARE-EARTH OXIDES Magnetic oxides are an extensive class of materials with a great variety of structures and properties. Regarding magnetic ordering, they usually present complex behaviors, including non-collinear magnetism, ferrimagnetism, or multiple phase transitions, often accompanied by structural transformations. Moreover, the presence of more than one magnetic atom in the structure could lead to a distinctive ordering for each species. For instance, there are many oxides that include a rare-earth element and a transition metal (Mn, Cr, Fe, etc.). In these cases, the interplay between 3d and 4f electrons usually plays a major role in the magnetic properties of the compounds, leading to unique features. ΔSiso ΔSiso From the point of view of the synthesis, oxides follow production methods which clearly differ from those of intermetallic compounds. As a result, the fabrication of relatively large single crystals is usually possible. This feature makes these single crystal potential candidates for rotating magnetocaloric devices in which the refrigeration driving force is created by rotating a strongly anisotropic sample inside a constant magnetic field rather than inducing phase transition on an isotropic material upon changing the modulus of the applied magnetic field. In the case of materials for rotating magnetocaloric applications, the difference between the values obtained along two well-defined crystallographic directions is the key parameter to maximize to obtain an appropriate material, and it is denoted as rotational . The larger the difference between two directions, the larger the refrigerant capacity will be when rotating the sample inside a magnetic field. For the transition temperatures of oxides, they could range from a few K to more than 1000 K. Most of them undergo phase transitions at very low temperatures, below 10 K, but there are still many examples with higher transition temperatures, such as manganites, ferrites, spinels, etc. In this section, we focus on those with transition temperatures in our target range suitable for hydrogen liquefaction applications. Our discussion proceeds in increasing order of structural complexity, beginning with simple oxides with one metal in the anion (i.e., RCrO4, RTiO3, RVO4, etc.), and relatively simple structures, such as perovskite and zircon types. Finally, we discuss double oxides that include two metal atoms in the anion site and finalize with garnets and other complex oxides. |ΔSiso| ΔTad Several simple oxides with general stoichiometries of RMO3 and RMO4 have been investigated in the framework of magnetocaloric effect. RMO3 compounds, such as RCrO3, RFeO3, RTiO3, RMnO3 RVO3, display perovskitetype structure whereas RMO4 compounds, like RCrO4 or RVO4, crystallize within the tetragonal zircon-type symmetry. In addition, some spinel oxides could be included in this group. They are the simplest oxides showing a remarkable MCE. To the best of our knowledge, there is no other oxide simpler than these ternary ones with a remarkable MCE, except the notable EuO. This binary oxide crystallizes with a NaCl-type crystal structure and behaves as a ferromagnet with a Curie temperature of 69 K. For an applied field of 5 T, it shows of 17.5 J kg−1 K−1, of 6.8 K and RCP of 665 J kg−1.247 Investigated chromite compounds are of the RCrO3 type, with R = Sm, Dy, Ho, Er, Yb.248-250 They show antiferromagnetic order and some of them display appropriate transition temperatures like HoCrO3 or ErCrO3, whose transition temperatures are 20 and 10 K, respectively. In general, these compounds show a moderate MCE magnitude, except the aforementioned ErCrO3, with a remarkable value of -13 J kg−1 K−1 and an associated RC of 419 J kg−1.249 |ΔSiso| Single crystals of rare-earth orthoferrites (RFeO3) with orthorhombically distorted perovskite crystal structure have been investigated due to their strong anisotropy along different crystallographic directions.251-253 The values of rotational isothermal entropy changes between 10 and 20 J kg−1 K−1 for an applied field of 5 T can be achieved in these materials. Polycrystalline samples of GdFeO3 have also been investigated,254 where they exhibit very large values, over 30 J kg−1 K−1 for 5 T, but at around 5 K, which is too low for direct applications in hydrogen liquefaction refrigeration. Manganites with the general formula of RMnO3 are a well-known class of compounds for the magnetocaloric community since there are hundreds of them fully characterized.260 Although rare-earth free manganites usually display near-room temperature phase transitions, those with rare-earth elements may have much lower transition temperatures. The investigated RMnO3 includes the magnetocaloric characterization of single crystals where R = Nd,261 Dy,262 Tb,263 Ho264 and Tm.265 Another important feature of manganites is that their transition temperatures can be easily tuned by element substitution or pressure. As an example, we can mention the La0.65Ca0.35Ti1-x MnxO3 system in which the Curie temperature linearly varies from ~100 K for x=0 to ~40 K for x=0.4.266 Unfortunately, the MCE magnitude in rare-earth manganites is much weaker than the observed for other related oxides. ΔSiso |ΔSiso| ΔTad Rare-earth titanates (RTiO3) present very interesting magnetocaloric features. They display a relatively simple ferromagnetic ordering compared with other similar oxides and transition temperatures in the range of 30-70 K in most cases. Y Su, et al.267 systematically studied the MCE of RTiO3 compounds with R = Dy, Ho, Er, Tm, and Yb, revealing very promising properties. The maximum values are larger than 10 J kg−1 K−1 accompanied by remarkable RCP values that could be larger than 400 J kg−1. Similar values have been reported for GdTiO3 single crystals.268 Conversely, a distinctive behavior has been observed for EuTiO3, which orders antiferromagnetically at only 5 K and shows huge and values of 40 J kg−1 K−1 and 16 K respectively.269,270 It is worth noting that the MCE of metavanadates (RVO3) has not been studied with the exception of HoVO3, whose magnetic properties are clearly distinctive. It undergoes several phase transitions, either due to the Ho3+ ion ordering or structural transitions, giving rise to a table-like MCE which spans over a broad temperature range.271 ΔSiso On the other hand, some rare-earth chromates (RCrO4) have been studied for R = Gd,255,272,273 Dy,274 Ho255,274 and Er.272 They crystallize in the tetragonal zircon-type structure and exhibit complex magnetic properties due to the strong competition between ferromagnetic and antiferromagnetic superexchange interactions of 3d and 4f spins. Overall, they behave as ferromagnets but with some anomalies and often with field-induced metamagnetic transitions. Nonetheless, they present remarkable over 20 J kg−1 K−1 for an applied field of 5 T, as shown in Figure 6A. Notably, other RCrO4 compounds also exhibit transition temperatures between 10 and 25 K and complex magnetic properties, such as non-collinear magnetic ordering.275,276 Hence, they represent an interesting group of compounds for further investigation of their magnetocaloric properties. ΔSiso ΔTad Rare-earth vanadates (RVO4) are also a particularly interesting family of magnetic oxides. They present excellent magnetocaloric properties but at very low temperatures that are not completely suitable for hydrogen liquefaction purposes.256,277 This is because their antiferromagnetic order typically occurs below 5 K (see Figure 6B), but their curves are exceptionally broad, leading to a remarkable MCE even at temperatures around 20 K, at least for high fields.277 A similar behavior is observed for . In spite of this, there are still a few compounds worth highlighting. On the one hand, HoVO4 displays the maximum MCE around 15 K. As it is assumed that its antiferromagnetic ordering occurs at very low temperatures (<1 K), this abnormal feature might be attributed to the crystal-field-split effect of Ho3+ ions.277 On the other hand, compounds such as TbVO4 or DyVO4 show excellent tablelike MCE associated to the combination of the AF ordering at 14 K with a subsequent structural transformation from the original tetragonal symmetry to another orthorhombic phase, which takes place at 33 K257,278 leading to a large conventional and rotating MCE (see Figure 6B). Because of their large relative cooling power and good performance over a broad temperature range, these compounds are particularly interesting. Double oxides with more complex stoichiometries, such as RM2O5, R2M2O5, RM2O6, R2M2O6 (typically with double perovskite structure) or R2M2O7, also deserve highlights from the magnetocaloric point of view. |ΔSiso| Balli, et al. have studied the rotating MCE of HoMn2O5279 and TbMn2O5280 due to their strong anisotropy, finding remarkable rotating values over 10 J kg−1 K−1. Moreover, TbMn2O5 exhibits a giant rotating MCE when rotated around the b axis, achieving temperature changes up to 18.7 K.280 Several cuprates with similar stoichiometries (i.e., R2Cu2O5 and R2BaCuO5) have been investigated but they usually display inverse MCE and their performance is Materials REVIEW The Innovation Materials 1(3): 100045, December 13, 2023 9 the Pr7Pd3 Compound. J. Supercond. Nov. Magn. 31 , 2573−2577. Singh, N.K., Kumar, P., Mao, Z., et al. (2009). Magnetic, magnetocaloric and magnetoresistance properties of Nd7Pd3. J. Phys. Condens. Matter 21 , 456004. 146. Jensen, W.B. (2003). 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ACKNOWLEDGMENTS Work funded by PID2019-105720RB-I00/AEI/10.13039/501100011033, Air Force Office of Scientific Research (FA8655-21-1-7044), the Clean Hydrogen Partnership and its members within the project HyLICAL (Grant No. 101101461), the European Innovation Council, funded by the European Union, via project CoCoMag (Grant no. 101099736), and the Research Council of Norway within project LIQUID-H. C. R.-M. acknowledges financial support by the Ramón y Cajal program of the Spanish Ministry of Science and REVIEW 18 The Innovation Materials 1(3): 100045, December 13, 2023 www.the-innovation.org/materials Innovation (Ref. RYC2021-031176-I). J.Y.L acknowledges EMERGIA 2021 fellowship from Junta de Andalucía (Ref. EMC21_00418). AUTHOR CONTRIBUTIONS C.R.-M., J.Y.L, J.R.-L. and L.M.M.-R. collected the data and revised the literature necessary for this work. C.R.-M and J.Y.L wrote the original manuscript. J.Y.L made the figures with some assistance from J.R.-M and L.M.M.-R. V.F. supervised all the tasks and revised the manuscript. All authors revised and contributed to the final edition of this article and approved the final submitted version. DECLARATION OF INTERESTS The authors declare no competing interests. SUPPLEMENTAL INFORMATION It can be found online at https://doi.org/10.59717/j.xinn-mater.2023.100045 LEAD CONTACT WEBSITE The lead contact website is https://personal.us.es/vfranco Materials REVIEW The Innovation Materials 1(3): 100045, December 13, 2023 19