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[Koichi Matsumoto](https://orcid.org/0000-0003-1141-5239), Masaki Horie, Hironori Hasegawa, Kazuhiro Ishikawa, Shuhei Yamazaki, [Hideaki Kitazawa](https://orcid.org/0000-0002-9756-2311), [Akiko T. Saito](https://orcid.org/0000-0001-5920-5965), [Takenori Numazawa](https://orcid.org/0000-0003-1828-4972)

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[Giant magnetocaloric effect of divalent europium-based oxide composites of Eu2TiO4 and Eu3Ti2O7 for cryogenic temperature magnetic refrigeration](https://mdr.nims.go.jp/datasets/9b1ee698-db3c-41be-b5e7-593b5450b60f)

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Giant magnetocaloric effect of divalent europium-based oxide composites of Eu2TiO4 and Eu3Ti2O7 for cryogenic temperature magnetic refrigerationViewOnlineExportCitationRESEARCH ARTICLE |  JULY 15 2025Giant magnetocaloric effect of divalent europium-basedoxide composites of Eu2TiO4 and Eu3Ti2O7 for cryogenictemperature magnetic refrigerationKoichi Matsumoto   ; Masaki Horie; Hironori Hasegawa; Kazuhiro Ishikawa; Shuhei Yamazaki;Hideaki Kitazawa  ; Akiko T. Saito  ; Takenori Numazawa J. Appl. Phys. 138, 033901 (2025)https://doi.org/10.1063/5.0278479Articles You May Be Interested InLarge reversible magnetocaloric effect in TmTiO3 single crystalJ. Appl. Phys. (March 2012)Octahedral tilt independent magnetism in confined GdTiO3 filmsAppl. Phys. Lett. (March 2018)Structural, magnetic, and electronic properties of GdTiO3 Mott insulator thin films grown by pulsed laserdepositionAppl. Phys. Lett. (October 2014) 18 August 2025 09:55:45https://pubs.aip.org/aip/jap/article/138/3/033901/3352911/Giant-magnetocaloric-effect-of-divalent-europiumhttps://pubs.aip.org/aip/jap/article/138/3/033901/3352911/Giant-magnetocaloric-effect-of-divalent-europium?pdfCoverIconEvent=citejavascript:;https://orcid.org/0000-0003-1141-5239javascript:;javascript:;javascript:;javascript:;javascript:;https://orcid.org/0000-0002-9756-2311javascript:;https://orcid.org/0000-0001-5920-5965javascript:;https://orcid.org/0000-0003-1828-4972https://crossmark.crossref.org/dialog/?doi=10.1063/5.0278479&domain=pdf&date_stamp=2025-07-15https://doi.org/10.1063/5.0278479https://pubs.aip.org/aip/jap/article/111/7/07A925/387485/Large-reversible-magnetocaloric-effect-in-TmTiO3https://pubs.aip.org/aip/apl/article/112/13/132407/34825/Octahedral-tilt-independent-magnetism-in-confinedhttps://pubs.aip.org/aip/apl/article/105/17/172402/1022674/Structural-magnetic-and-electronic-properties-ofhttps://e-11492.adzerk.net/r?e=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&s=J2XZmMb1qaD2VVfYcJKfP1VlVFQGiant magnetocaloric effect of divalent europium-based oxide composites of Eu2TiO4 and Eu3Ti2O7for cryogenic temperature magnetic refrigerationCite as: J. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479View Online Export Citation CrossMarkSubmitted: 30 April 2025 · Accepted: 24 June 2025 ·Published Online: 15 July 2025Koichi Matsumoto,1,a) Masaki Horie,1 Hironori Hasegawa,1 Kazuhiro Ishikawa,2 Shuhei Yamazaki,2Hideaki Kitazawa,3 Akiko T. Saito,3 and Takenori Numazawa3AFFILIATIONS1Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan2Corporate Fine Ceramics Group, Kyocera Corporation, Kyoto-shi, Kyoto 612-8501, Japan3National Institute for Materials Science (NIMS), Tsukuba 305-0003, Japana)Author to whom correspondence should be addressed: k.matsu@staff.kanazawa-u.ac.jpABSTRACTFor cryogenic temperature magnetic refrigeration, we focused on materials containing Eu2+ ions and synthesized sintered composite materialscomprising Eu2TiO4 and Eu3Ti2O7. Eu3Ti2O7 and Eu2TiO4 exhibited second-order phase transitions between the paramagnetic and fer-romagnetic states at 7 and 8 K, respectively. The magnetocaloric effect was evaluated from magnetization and specific heat. It was shownthat Eu2+ ions behave similarly to free ions with J = 7/2. The maximum magnetic entropy change per unit volume exceeded 0.3 J/cm3K ata magnetic field of 5 T. The Carnot cycle at the hydrogen liquefaction temperature was evaluated using the obtained entropy temperaturediagram. It was found that the cooling capacity is several times higher than that of known materials such as Gd3Ga5O12, (Dy0.8Gd0.2)3Al5O12,and GdTiO3. It was also shown that the present composite materials are useful for extending the operating temperature range of the adiabaticdemagnetization refrigerator. These results indicate that Eu2TiO4 and Eu3Ti2O7 composites are promising magnetic refrigerants for cryogenicmagnetic refrigeration.© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/). https://doi.org/10.1063/5.0278479I. INTRODUCTIONMagnetic refrigeration has emerged as a leading candidate toreplace conventional gas expansion refrigerators. This approach uti-lizes the magnetocaloric effect (MCE), a phenomenon in which achange in an externally applied magnetic field causes a correspond-ing temperature variation in a magnetic material (the refrigerant).The concept of utilizing the MCE for solid-state cooling was ini-tially proposed by Debye1 and Giauque.2 Since that time, the fieldhas undergone substantial advancements. The potential benefits ofhigh efficiency, reduced environmental impact, compact size, andsilent operation have prompted substantial research in novel mag-netic materials and refrigeration system architectures, spanning awide temperature range.3–6Hydrogen, a clean and environmentally benign energy carrier,offers a promising solution to growing energy demands. Theutilization of this technology serves to mitigate the release of green-house gases and pollutants into the atmosphere. Liquid hydrogen,characterized by its high density, is considered an optimal mediumfor storage and transportation.7,8 Although Joule–Thomson expan-sion remains the prevailing standard for hydrogen liquefaction,magnetic cooling has garnered considerable attention due to itsability to improve energy efficiency.Significant advancements in the field of hydrogen liquefactionhave been achieved through the development of magnetic refrigera-tion technology. Numazawa et al.,9,10 Matsumoto et al.,11 andOhira et al.12 have demonstrated successful hydrogen liquefactionusing the Carnot cycle. In the recent study, Kamiya et al.13 reportedthe successful implementation of liquefaction using an active mag-netic regenerator (AMR) cycle.In the liquefaction stage, the Carnot magnetic refrigerator(CMR) was utilized, employing a heat pipe to condense theJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479 138, 033901-1© Author(s) 2025 18 August 2025 09:55:45https://doi.org/10.1063/5.0278479https://doi.org/10.1063/5.0278479https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0278479http://crossmark.crossref.org/dialog/?doi=10.1063/5.0278479&domain=pdf&date_stamp=2025-07-15https://orcid.org/0000-0003-1141-5239https://orcid.org/0000-0002-9756-2311https://orcid.org/0000-0001-5920-5965https://orcid.org/0000-0003-1828-4972mailto:k.matsu@staff.kanazawa-u.ac.jphttps://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://doi.org/10.1063/5.0278479https://pubs.aip.org/aip/japhydrogen gas directly on the surface of the magnetic material. Thismethod has been demonstrated to achieve significantly higherthermal efficiency in comparison with the conventional approachthat utilizes the Joule–Thomson valve. The magnetic refrigerantemployed in this CMR design must exhibit a substantial magneto-caloric effect (MCE) coupled with robust chemical stability againsthydrogenation. To meet these criteria, Ohira used a single crystalgadolinium gallium garnet, Gd3Ga5O12 (GGG)12 and our groupselected a ceramic Dy-substituted gadolinium aluminum garnet,(Dy0.8Gd0.2)3Al5O12 (DGAG)9 as the magnetic refrigerant.The operation of astronomical instruments, such as the transi-tion edge sensor (TES), requires cooling methods that can attainsub-Kelvin temperatures to ensure optimal sensitivity. In order tofacilitate continuous cooling at these temperatures, the cryogenicgroup at NASA’s Goddard Space Flight Center (GSFC) has devel-oped a multi-stage continuous adiabatic demagnetization refrigera-tor (ADR).14,15 The capabilities of the technology have beendemonstrated by a four-stage cascaded ADR (CADR) operatingbetween 50 mK and 4.5 K. In the higher temperature stages of theseADRs, GGG is typically employed as the magnetic refrigerant.Gadolinium lithium fluoride (GdLiF4, GLF) has also been exploredas a potential alternative in these stages because of its attractivemagnetic characteristics.16,17Numerous magnetic materials have been investigated aspotential refrigerants for cryogenic temperatures.3–6,18,19 The selec-tion of appropriate materials that have large magnetic entropychange (ΔSm) and proper transition temperature (Tc) is crucial formagnetic refrigeration.Gadolinium (Gd3+) ions are of interest due to their substantialmagnetic moment (J = 7/2). The absence of spin–orbit coupling inGd3+ generally leads to highly degenerated localized magneticmoments within the crystal lattice, allowing these moments to bemaintained even at low temperatures.20 GGG is used as a standardmagnetic refrigerant in cryogenic temperatures.19,21–24 A series ofFe-modified gadolinium gallium garnets (Gd3(Ga1−xFex)5O12,GGIG) was demonstrated to exhibit a larger ΔSm than that of GGGat 20 K.25,26 Polycrystalline plates and spheres composed of GGG,DGAG, and GGIG were synthesized and examined in magneticrefrigerators.10,11,19Furthermore, the MCE has been extensively studied in perov-skite oxides such as GdTiO3 (GTP),27 GdAlO3 (GAP),28,29DyTiO3,30 HoTiO3,31 TmTiO3,32 and EuTiO3 (ETP).33,34In this study, we investigated the potential of divalent euro-pium (Eu2+) compounds as magnetic refrigerants. The 4f 7 electronconfiguration (J = 7/2) of Eu2+ ions has been shown to minimizecrystalline electric field effects and magnetic anisotropy, therebypromoting a large and isotropic MCE. The ferromagnetic chalco-genides EuO (Tc = 69 K)35 and EuS (Tc = 18 K), both with NaClstructures, have been previously studied for their substantialMCE.36–38In the ternary Eu–Ti–O system, McCarthy et al. identifiedseveral compounds.39 ETP, a multiferroic with a cubic perovskitestructure (a = 3.90 Å) exhibits G-type antiferromagnetic ordering at5.5 K, and its magnetic properties have been studied.40–43 The largeMCE has also been reported.34Eu2TiO4 and Eu3Ti2O7 are distinguished by their layeredperovskite structures, which are characteristic of the Ruddlesden–Popper phases. The general formula for these phases is written asAn−1A02BnX3n + 1, where A, A0, and B represent cations, X is ananion, and n designates the number of octahedral layers in theperovskite-like stack. The crystal structure of Eu2TiO4 (n = 1)exhibits a K2NiF4-type structure (space group I4/mmm) with atetragonal unit cell (a = 3.883 Å and c = 12.523 Å) containing twoformula units. That of Eu3Ti2O7 (n = 2) also exhibits a tetragonalstructure (space group I4/mmm, a = 3.90 Å, c = 20.28 Å) and con-sists of alternating layers of EuTiO3 and Eu2TiO4, with two non-equivalent Eu sites. The number of Eu2TiO4 sites is twice that ofEuTiO3 sites.44,45 The crystal structures of Eu2TiO4 and Eu3Ti2O7are depicted in Fig. 1.Magnetization (M) studies of ETP, Eu2TiO4, and Eu3Ti2O7have been conducted.46 Eu2TiO4 and Eu3Ti2O7 were found to beferromagnetic with Tc of 9 and 8.5 K, respectively. In addition,151Eu Mössbauer spectroscopy further revealed Eu2TiO4 to be fer-romagnets with a Tc of 7.8 K, suggesting a ferrimagnetic orderingdue to positive exchange interaction between inequivalent EuTiO3and Eu2TiO4 sublattices.40,47Eu2TiO4 and Eu3Ti2O7 were identified as promising magneticrefrigerants for cryogenic applications due to their suitable transi-tion temperatures and ferromagnetic interactions. Consequently,composite ceramic materials comprising Eu2TiO4 and Eu3Ti2O7were synthesized. The MCE of these composites, as evaluated fromM and specific heat (C) measurements, exhibits a substantialincrease compared to that of other oxide materials. Furthermore,the volumetric cooling capacity of our composites in a Carnot cyclefor hydrogen liquefaction was found to be several times larger thanthat of GGG and DGAG. These materials also exhibit potential forextending the operating temperature range of ADRs to highertemperatures.II. EXPERIMENTAL PROCEDUREThe synthesis of ceramic composite materials was conductedas follows: Eu2O3 and TiO powders were weighed out in severalratios near 1:1. Subsequently, the raw powders were meticulouslymilled in isopropyl alcohol using a ball mill. Subsequent to milling,an organic binder was incorporated into the mixture, and themixture was granulated while volatilizing the isopropyl alcohol.The granulated mixture was subsequently pressurized and moldedat 147MPa to yield disk-shaped pellets with a diameter of 12 mmand a thickness of 3 mm. The preparation of the ceramic sampleswas conducted with the heating of the pellets at two distinct tem-peratures: 1400 °C for samples 1 and 3 and 1500 °C for sample 2.Samples for magnetization and specific heat measurements werecut from these sintered pellets.Due to difficulties in acquiring a single-phase material, thedecision was made to synthesize composite samples. Three distinctcompositions were prepared: sample 1, composed of Eu3Ti2O7 andEu2O3; sample 2, composed of Eu2TiO4 and Eu3Ti2O7; and sample3, composed of Eu2TiO4, Eu3Ti2O7, and Eu2O3. As illustrated inFig. 1, the powder XRD pattern of sample 3 reveals the presence ofthree crystalline phases. As shown in Table I, the compositionratios for each sample are determined by means of Rietveldrefinement.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479 138, 033901-2© Author(s) 2025 18 August 2025 09:55:45https://pubs.aip.org/aip/japThe synthesis of high-density sintered pellets with low poros-ity was successfully achieved. The bulk densities of the sinteredsamples were determined using Archimedes’ principle. The mea-sured bulk densities are also presented in Table I.The temperature dependences of magnetization (M–T) weremeasured using a Quantum Design SQUID magnetometer MPMSin applied magnetic fields ranging from 0.1 to 5 T. Rectangular rod-shaped samples with dimensions of 0.55 × 0.55 × 3.30 mm3 wereused for these measurements. The magnetic field was applied alongthe longitudinal direction of the rods to minimize demagnetizationeffects.Specific heat measurements were conducted using a thermalrelaxation method with a Quantum Design PPMS. Plate-shapedsamples with dimensions of 2.0 × 2.0 × 1.1 mm3 were used for themeasurements in the temperature range of 2–300 K.III. RESULTSA. Specific heat and entropyFigure 2 shows the temperature dependence of C for threesamples in the zero magnetic field. The sharpness of these peaksindicates the high quality of the synthesized materials. In Eu2O3,europium exists as Eu3+ ion, which has a significantly smaller mag-netic moment compared to the Eu2+ ion. Consequently, the mag-netic specific heat of Eu2O3 is considered negligible, and its totalheat capacity is primarily attributed to the lattice contribution.49,50Sample 1 is mainly composed of Eu3Ti2O7, so the specific heatpeak at 7 K is attributed to Eu3Ti2O7. Two different peaks areTABLE I. Composition ratios of Eu2TiO4, Eu3Ti2O7, and Eu2O3 constituting samples1, 2, and 3. Bulk density is also shown for each sample.SampleEu2TiO4(wt. %)Eu3Ti2O7(wt. %)Eu2O3(wt. %)Bulk density(g/cm3)1 0.0 80.0 20.0 7.052 56.2 43.8 0.0 6.993 44.4 37.6 18.0 7.01FIG. 2. Temperature dependence of specific heat for samples 1, 2, and 3 in thezero magnetic field. The dashed line shows the lattice specific heat CL obtainedfrom a Debye model fit.FIG. 1. (Left) crystal structures of Eu2TiO4 and Eu3Ti2O7 drawn using VESTA.48 (Right) x-ray powder diffraction pattern of the composite (sample 3). Vertical bars repre-sent diffraction angles of Eu2TiO4, Eu3Ti2O7, and Eu2O3.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479 138, 033901-3© Author(s) 2025 18 August 2025 09:55:45https://pubs.aip.org/aip/japobserved in samples 2 and 3, which have Eu3Ti2O7 and Eu2TiO4.Therefore, we consider that the specific heat peak at 8 K isattributed to Eu2TiO4. The transition temperatures attributedto Eu3Ti2O7 and Eu2TiO4 are both lower relative to those in theliterature,46 respectively, but the high-low relation of the Tc isthe same. Therefore, the specific heat peaks at 7 and 8 K areidentified as those of Eu3Ti2O7 and Eu2TiO4, respectively.The slight difference in the Tc values from the literature may bedue to sample dependence on oxygen deficiency or other factors.The relative magnitudes of the peaks are qualitatively consistentwith the compositional ratios of the samples. Above 20 K, the Cof each sample increases with temperature and converges, indi-cating that the lattice heat capacity becomes the dominant con-tribution in this temperature range.The total entropy (S) was calculated by integrating C/T withrespect to temperature in a constant magnetic field (H) asΔS(T , H) ¼ðT0CT� �HdT: (1)Figure 3 presents the S of all the samples in the zero fieldcalculated using Eq. (1). The C data below 2 K were smoothlyextrapolated to 0 at absolute zero before integration. A clear releaseof magnetic entropy (Sm) is observed below 10 K for each sample.As discussed earlier, the increase in S above 20 K is attributed tothe lattice contribution. The total S appears to correlate withthe amount of Eu2TiO4 and Eu3Ti2O7 in each sample. The totalamount of Eu2+ ions (NEu2+) was determined from the compositionratio in Table I, yielding values of 3:62� NA, 4:68� NA, and3:84� NA (NA, the Avogadro constant) per kilogram for samples 1,2, and 3, respectively. The theoretical magnetic entropy Sm for1 mol of ions with spin J is given by R ln (2J þ 1), where R is theideal gas constant. Then, this theoretical value for each sample(NEu2þ � R ln (2J þ 1)) is indicated as a horizontal arrow in Fig. 3for each sample. The measured Sm values are in good quantitativeagreement with these theoretical predictions.In order to isolate the magnetic contribution of the Eu2+ ionto the total S, we fitted C above 20 K using the Debye model. Thisallowed us to extract the lattice specific heat (CL) and subsequentlydetermine the magnetic specific heat. The inset in Fig. 3 showsthe temperature dependence of Sm per Eu2+ ion. The dashed linerepresents the theoretical value of kB ln (2J þ 1) for a free ion withJ = 7/2, where kB is Boltzmann’s constant. The Eu2+ ions releasealmost 100% of their theoretical magnetic entropy during the mag-netic transition for each sample. The ionic valence of the Ti atomis inferred to be in the tetravalent state, which has less contributionto magnetic ordering.B. Magnetization and entropy changeFigure 4 shows the temperature dependence of M for samples1, 2, and 3, respectively, in applied magnetic fields up to 5 T. Ineach constant field, the M increases rapidly around 10 K withdecreasing temperature. Higher M values were observed forsamples with the lower Eu2O3 content. However, while two distinctpeaks were observed in the C data in Fig. 2, the two correspondingferromagnetic transitions of Eu2TiO4 and Eu3Ti2O7 are not clearlyobserved in the M–T curves. No stepwise increase in M wasobserved. This is probably due to the smooth increase in M charac-teristic of the second order phase transition, coupled with the closeproximity of the two Tc. A comparison of the temperature deriva-tive of the magnetization @M@T� �at 0.1 T shown in Fig. 5 reveals asingle dip for each sample, with the dip temperature varyingaccording to the composition ratio. The magnetic moment ofEu2O3 is considered negligible compared to that of Eu2TiO4 andEu3Ti2O7.49,50Figure 6 shows the inverse magnetic susceptibilities of ourcomposite samples at 0.1 T. Above Tc, the inverse susceptibilitiesincrease linearly with increasing temperature, consistent with theCurie–Weiss behavior. Then, using a rough approximation thatassumes two close phase transitions as a single transition, weapplied a Curie–Weiss fit to this high temperature region to esti-mate the effective magnetic moment per Eu2+ ion and the para-magnetic Curie temperature. The obtained effective magneticmoments per Eu2+ ion were 7.8, 7.9, and 8:0 μB (Bohr magneton)for samples 1, 2, and 3, respectively. The corresponding paramag-netic Curie temperatures were 7.6, 9.2, and 8.6 K. These effectivemagnetic moments are in reasonable agreement with the theoreticalvalue of 7:9 μB expected for a J = 7/2 spin state. This agreementfurther supports the conclusion that the Eu2+ ion has a J = 7/2magnetic moment and the ionic valence of the Ti atom is in thetetravalent state, which has no magnetic moment under this roughassumption.At low temperatures and high magnetic fields, M tends to sat-urate. The saturation magnetization for an ion with spin J is givenby gμBJ, where g is the Landé g-factor. The electron configurationof Eu2+ ion results in g ¼ 2. Assuming that the saturationFIG. 3. Temperature dependence of entropy for samples 1, 2, and 3 in the zeromagnetic field. Horizontal arrows indicate the theoretical Sm caused by Eu2TiO4and Eu3Ti2O7 for each sample. Vertical arrows indicate Tc of Eu2TiO4 andEu3Ti2O7. The inset shows magnetic entropy Sm per Eu2+ ion for each sample.The dashed line in the inset represents the theoretical Sm for a free ion withJ = 7/2 (see text for details).Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479 138, 033901-4© Author(s) 2025 18 August 2025 09:55:45https://pubs.aip.org/aip/japmagnetization is primarily due to the Eu2+ ions present in Eu2TiO4and Eu3Ti2O7, the theoretical saturation magnetization values werecalculated as NEu2þ � gμBJ . These values are indicated by arrows inFig. 4. The measured saturation magnetization values are in goodquantitative agreement with these theoretical predictions, confirm-ing the important role of Eu2+ ions in the magnetic properties ofthese materials.The magnetic entropy change (ΔSm) was evaluated from aseries of the M–T curves according to the Maxwell relationΔSm(T , H) ¼ðH0@M@T� �HdH, (2)where H is the applied magnetic field. Figure 7 shows −ΔSm of ourcomposites. The −ΔSm curve exhibits a characteristic caret-likeshape, consistent with second order magnetic phase transitions.FIG. 4. Temperature dependence of the magnetization in applied fields of 0.1, 0.2, 0.4, 0.6, 0.8, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5 T. Arrows indicate the calculated satura-tion magnetization for Eu2+ free ions (see text for details).FIG. 5. Temperature derivative of magnetization @M@T as a function of temperaturein 0.1 T for samples 1, 2, and 3.FIG. 6. Inverse magnetic susceptibility (1/χ) as a function of temperature forsamples 1, 2, and 3.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479 138, 033901-5© Author(s) 2025 18 August 2025 09:55:45https://pubs.aip.org/aip/japFigure 8 shows the −ΔSm at 5 T for all three samples. −ΔSmshows a peak near the respective Tc of each sample. The maximum−ΔSm values of samples 1 and 3 are nearly identical, which is con-sistent with their similar total content of Eu2TiO4 and Eu3Ti2O7.The peak temperature for sample 1 is lower than that of sample 3,reflecting the presence of Eu3Ti2O7 in sample 1, which has a lowerTc. As observed in M, the magnitude of the −ΔSm correlates withthe amount of Eu2O3. Sample 2 without Eu2O3 exhibits the largest−ΔSm, reaching a maximum value of 43.8 J/kg K. At the hydrogenliquefaction temperature 20.3 K, the −ΔSm for sample 2 is stillsignificant value of 19.4 J/kg K. These results demonstrate that ourcomposite materials exhibit giant MCE and are promising materialsamong oxide magnetic refrigerants. The data confirm that Eu2TiO4and Eu3Ti2O7 are responsible for the observed MCE and that mini-mizing Eu2O3 is crucial for maximizing performance. The differ-ence in −ΔSm between samples 1 and 3 in Fig. 8 suggests thatEu2TiO4 exhibits a greater entropy change at high temperaturescompared to Eu3Ti2O7, which is consistent with its higher Tc.C. Entropy temperature diagram and adiabatictemperature changeFigure 9 shows the entropy-temperature diagram for compositesample 2, which exhibits the largest MCE among our composites. Theentropy at various magnetic fields S(T, H), was calculated by addingΔSm(T,H) (determined in Sec. III B) to the zero field entropy S(T,0)(from Sec. III A), using the relation S(T , H) ¼ S(T , 0)þ ΔSm(T , H).An example of a Carnot cycle is shown as a solid rectangle. Furtherdiscussion follows in Secs. IV B and IV C.The adiabatic demagnetization process can be evaluated usingan entropy–temperature diagram. As illustrated in Fig. 9, duringadiabatic demagnetization, the temperature of the materialdecreases from an initial temperature (Ti) to a final temperature(Tf ) as the magnetic field is reduced from an initial field (Hi) of 5 Tto zero. The Tf values obtained under various conditions areplotted on the left side of Fig. 10. The adiabatic temperaturechanges (ΔTad ¼ Ti � Tf ) are shown on the right side of Fig. 10.ΔTad exhibits a peak value of 15.5 K when Ti is 25.5 K under a 5 Tfield, resulting in a final temperature of 10 K. A final temperatureof 20 K can be achieved from a Ti of 29.5 K using a 5 T field. Theseresults suggest that composite sample 2 has significant potential asa refrigerant material for hydrogen liquefaction and produces sub-cooled liquid hydrogen.FIG. 7. Magnetic entropy change −ΔSm as a function of temperature for the composite samples in various applied magnetic fields (0.1, 0.2, 0.4, 0.6, 0.8, 1, 1.5, 2, 2.5, 3,3.5, 4, 4.5, and 5 T), calculated from magnetization data.FIG. 8. Temperature dependence of −ΔSm at 5 T for the composite samples.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479 138, 033901-6© Author(s) 2025 18 August 2025 09:55:45https://pubs.aip.org/aip/japIt is important to note that evaluating entropy necessitatesintegrating specific heat and magnetization data, which inherentlyintroduces some integration-related errors. In Sec. IV, we willcompare the entropy of various materials. A certain degree of erroris unavoidable because these calculations rely on entropy changes,specific heats, and other values derived from the existing literature.IV. DISCUSSIONA. Comparison of magnetic entropy change with otheroxide magnetic refrigerantsIn this section, we compare the performance of our compositematerial with other oxide magnetic refrigerants such as garnets andperovskites. Due to the limited available volume in high magneticfield applications, a comparison based on volumetric entropychange is particularly important. Figure 11 shows the temperaturedependence of −ΔSm at 5 T for several oxide materials: GGG,19,21,22DGAG,9,19 GTP,27 ETP,34 GAP,28,29 and our composite sample 2.Our composite sample 2 exhibits the largest −ΔSm in the tempera-ture range from 7 to 26 K, demonstrating a significant advantageover these other oxide refrigerants. The maximum volumetric−ΔSm achieved by sample 2 exceeds 0.3 J/cm3K. It is worth notingthat the bulk density was used to calculate the volumetric −ΔSm forsample 2, reflecting its composite sintered nature. For the othermaterials, theoretical densities derived from their crystal structurewere used.Our composite sample 2 exhibits a significantly higher MCEthan the garnet refrigerant GGG, which is a common benchmarkmaterial in cryogenic magnetic refrigeration applications. DGAGhas also been used in experimental magnetic refrigerators forhydrogen liquefaction.9,10 Above 4 K, sample 2 outperforms bothGGG and DGAG. At 20 K, a key temperature for hydrogen lique-faction, the −ΔSm of sample 2 is about 3.7 times greater than thatof GGG.Perovskite oxides have been considered candidate refrigerantsfor hydrogen magnetic refrigeration due to their higher percentageof magnetic elements, potentially higher Tc compared to garnets,and chemical stability against hydrogenation. While GAP is anantiferromagnet whose MCE has been studied,28,29 our compositesamples exhibit a significantly larger MCE than GAP over nearlythe entire temperature range. ETP, which belongs to the sameEu-Ti-O system, exhibits an antiferromagnetic transition at 5.5 K.Our composites with Eu2TiO4 and Eu3Ti2O7 exhibit much larger−ΔSm than that of ETP34 above the Tc of EuTiO3. In particular, the−ΔSm of our sample 2 is approximately two times larger than thatof ETP34 at 20 K. This superior performance is attributed to thehigher Tc and ferromagnetic interactions present in our composites.GTP, with a Tc (33 K) near the boiling point of hydrogen (20 K),was also studied for its MCE.27 GTP undergoes a second orderparamagnetic–ferrimagnetic transition involving Gd3+ and Ti3+ions. As shown in Fig. 11, the −ΔSm of GTP peaks at 33 K, but itsvalue at 20 K is about half that of our sample 2. These comparisonsclearly demonstrate the superior performance of our Eu2TiO4 andFIG. 9. Temperature dependence of entropy S(T,H) of composite sample 2 in 0,1, 2, 3, 4, and 5 T. The solid rectangle represents an example of the Carnotcycle operating between TL = 20 K and TH = 22 K. The area of the rectangle rep-resented by the dashed lines corresponds to the amount of heat QL absorbedduring the isothermal demagnetization process. The solid arrow represents anexample of the adiabatic demagnetization process from Ti = 15 K and Hi = 5 T toTf and 0 T.FIG. 10. (Left) Tf in adiabatic demag-netization process as functions of Tifrom various Hi of 1, 2, 3, 4, and 5 T tozero. (Right) ΔTad as functions of Ti.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479 138, 033901-7© Author(s) 2025 18 August 2025 09:55:45https://pubs.aip.org/aip/japEu3Ti2O7 composite compared to other oxide magnetic refriger-ants. This superiority results from their relatively high Tc (close to10 K) and the presence of ferromagnetic interactions.The −ΔSm of our sample 2 is comparable to that of GLF at5 K and more than twice as large as that of GLF above 10 K.17 Thissuggests the potential for using our material in ADRs to extendtheir operating temperature range to higher temperatures, as will bediscussed in Sec. IV C.B. Cooling capacity in Carnot cycles for hydrogenliquefactionA Carnot cycle is represented by a rectangle on an entropy–temperature diagram. As illustrated in Fig. 9, a Carnot cycle forhydrogen liquefaction between TL = 20 K and TH = 22 K is shownas a rectangle represented by solid lines. The area of the rectanglerepresented by the dashed lines corresponds to the amount of heat(QL ¼ TL � jΔSj) absorbed during the isothermal demagnetizationprocess.The heat absorbed per unit volume by the magnetic refrigerantduring a Carnot cycle was calculated from the entropy–temperaturediagram for our composite sample 2 and several other oxide refriger-ants (GGG, DAGA, GTP, GAP, and ETP). Data were obtained fromthe literature and our own measurements for GGG,19,21,22 DGAG,9,19GTP,27 GAP,28,29 and ETP.34 Two Carnot cycle scenarios wereconsidered: one with a heat absorption temperature (TL) of 20 Kand a heat rejection temperature (TH) of 22 K and the other withTL = 20 K and TH = 25 K. The resulting cooling capacities arecompared in Fig. 12.A comparison of the QL in Carnot cycles (Fig. 12) and the−ΔSm (Fig. 11) highlights the crucial role of the temperature depen-dence of the zero-field entropy in achieving a wide temperaturespan and large cooling capacity. As shown in Fig. 9, the size of theCarnot cycle rectangle on the S–T diagram decreases significantlywhen the zero-field entropy increases rapidly due to lattice specificheat and/or Schottky specific heat from crystal field splitting, eventhough the −ΔSm is large. GTP is an example in which the zero-field entropy plays an important role. Our composite sample 2demonstrates approximately four times the cooling capacity ofGGG. This superior performance highlights the advantage of mag-netic refrigerants containing Eu2TiO4 and Eu3Ti2O7 for Carnotcycle operation compared to other oxide magnetic refrigerants.Recently, the use of subcooled liquid hydrogen has been pro-posed to reduce transfer loss of liquid hydrogen.51 In this concept,liquid hydrogen is cooled below 20 K. As shown in the S–T diagram(Fig. 9), our composite shows that the refrigeration capacity increaseswith decreasing operation temperature. The temperature dependenceof refrigeration capacity will be discussed in Sec. IV C. In addition tochemical stability against hydrogen, our composite offers an advan-tage over metal-based magnetic refrigerants.C. Characteristics of the composite material for thehigh temperature stage of adiabatic demagnetizationrefrigeratorThe S–T diagram shown in Fig. 9 suggests that the tempera-ture range with the highest refrigeration capacity for the compositematerial is close to the Tc. To evaluate the potential of our compos-ite as a material suitable for the high temperature stage of ADR, weanalyzed the temperature dependence of −ΔS obtained in a Carnotcycle. Figure 13 shows the volumetric −ΔS as a function of the heatabsorption temperature (TL). For comparison, data for standardmaterials such as GGG19,21,22 and GLF16,17 are also shown. Solidand dashed lines represent −ΔS values at 5 T calculated for Carnotcycles with temperature spans (ΔT) of 2 and 5 K, respectively.Our composite material exhibits the largest −ΔS at tempera-tures slightly above Tc. GLF exhibits a significantly larger −ΔSFIG. 11. Volumetric magnetic entropy change (−ΔSm) at 5 T for sample 2 com-pared with those of GGG, DGAG, GTP, ETP, and GAP.FIG. 12. Cooling capacity QL in a Carnot cycle for the composite sample 2 incomparison with GGG, DGAG, GTP, GAP, and ETP. Two cases were calculated:one with a heat absorbing temperature (TL) of 20 K and a heat rejection temper-ature (TH) of 22 K, and the other with TL = 20 K and TH = 25 K.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 033901 (2025); doi: 10.1063/5.0278479 138, 033901-8© Author(s) 2025 18 August 2025 09:55:45https://pubs.aip.org/aip/japcompared to GGG at temperatures below about 10 K. The −ΔS ofour composite material decreases below Tc. However, it remainslarger than that of GLF and GGG at temperatures above about 5 K.This crossover temperature exhibits a slight variation with theapplied magnetic field strength. These results indicate that the com-posite material is promising as a magnetic refrigerant for the hightemperature stage of ADR, enabling an increase in the heat rejec-tion temperature. Furthermore, as shown in Fig. 8, −ΔS tends toincrease at lower temperatures with the increasing Eu3Ti2O7content. This suggests that the material properties can be tailoredby adjusting the composition ratio.Magnetic refrigeration systems typically use bulk materials invarious shapes (plates, cylinders, and spheres). Ceramic materialsoffer the advantage of easy fabrication into various shapes, as dem-onstrated in previous studies.9–11,19 We have successfully synthe-sized ceramic samples of our composite material with a highrelative density. This ease of processing makes the materials devel-oped in this study particularly promising for practical applications.While single-phase materials of Eu2TiO4 and Eu3Ti2O7 werenot synthesized in this study, the individual MCE contributions ofeach phase remain an open question. The magnitude of exchangeinteractions (both nearest neighbor and next nearest neighbor),crystal field effects, and lattice specific heat in each phase are differ-ent so that further investigations are needed to understand theirMCE behavior in detail. This study has demonstrated that oxideferromagnets containing Eu2+ ions exhibit large MCE in the cryo-genic temperature range and are promising magnetic refrigerants.V. CONCLUSIONSThis study investigated the MCE in magnetic oxides contain-ing Eu2TiO4 and Eu3Ti2O7, focusing on the large magneticmoment of Eu2+ ions. Specific heat measurements revealed distinctpeaks at 8 and 7 K, corresponding to the transition temperatures ofEu2TiO4 and Eu3Ti2O7, respectively. The relative peak magnitudeswere consistent with the Eu2TiO4/Eu3Ti2O7 ratios in the samples.The observed magnetic entropy release was in good agreement withthe theoretical value for Eu2+ ion in a J = 7/2 free spin state and nomagnetic moment of Ti4+ ions. Similarly, the saturation magnetiza-tion was in agreement with the expected value for Eu2+ ions andTi4+ ions. The maximum volumetric magnetic entropy change ofour composite exceeded 0.3 J/cm3K, which is significantly higherthan that of established oxide magnetic refrigerants. The entropychange of our composite was about 3.7 times larger than that ofGGG at the hydrogen liquefaction temperature of 20 K. The spe-cific heat and magnetization results were combined to obtain anentropy–temperature diagram. Analysis of the entropy–temperaturediagram revealed that our material exhibits a cooling capacityseveral times higher than that of other oxide refrigerants (GGG,DGAG, GTP, GAP, and ETP) when implemented in a hydrogenliquefaction Carnot cycle. Our composite materials also showpotential for extending the operating temperature range of ADRs tohigher temperatures.ACKNOWLEDGMENTSThis work was supported by the JST-Mirai Program underGrant No. JPMJMI18A3, Japan. The authors appreciate Dr. HiroyaSakurai for useful discussions.AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsKoichi Matsumoto: Conceptualization (lead); Funding acquisition(lead); Investigation (lead); Methodology (lead); Project administra-tion (lead); Supervision (lead); Visualization (lead); Writing – origi-nal draft (lead); Writing – review & editing (lead). Masaki Horie:Formal analysis (equal); Investigation (equal). Hironori Hasegawa:Formal analysis (equal); Investigation (equal). Kazuhiro Ishikawa:Investigation (equal). Shuhei Yamazaki: Investigation (equal).Hideaki Kitazawa: Investigation (equal); Methodology (equal);Resources (equal); Writing – review & editing (equal).Akiko T. Saito: Investigation (equal); Methodology (equal);Writing – review & editing (equal). Takenori Numazawa: Projectadministration (equal); Resources (equal).DATA AVAILABILITYThe datasets generated and/or analyzed during the currentstudy are available from the corresponding author upon reasonablerequest.REFERENCES1P. Debye, “Einige Bemerkungen zur Magnetisierung bei tiefer Temperatur,”Ann. Phys. 386(25), 1154–1160 (1926).FIG. 13. Magnetic entropy changes in Carnot cycles with a temperature spanof 2 and 5 K as functions of heat absorbing temperature (TL) for the compositesample 2 in comparison with GGG and GLF. 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