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[Xin Tang](https://orcid.org/0000-0001-6762-6145), Yoshio Miura, [Noriki Terada](https://orcid.org/0000-0002-8676-5586), [Enda Xiao](https://orcid.org/0000-0002-4372-1575), Shintaro Kobayashi, Allan Döring, [Terumasa Tadano](https://orcid.org/0000-0002-8132-2161), [Andres Martin‐Cid](https://orcid.org/0000-0002-9711-288X), Takuo Ohkochi, Shogo Kawaguchi, [Yoshitaka Matsushita](https://orcid.org/0000-0002-4968-8905), [Tadakatsu Ohkubo](https://orcid.org/0000-0003-3548-1951), Tetsuya Nakamura, Konstantin Skokov, Oliver Gutfleisch, [Kazuhiro Hono](https://orcid.org/0000-0001-7367-0193), [Hossein Sepehri‐Amin](https://orcid.org/0000-0002-7856-7897)

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Control of Covalent Bond Enables Efficient Magnetic CoolingRESEARCH ARTICLEwww.advmat.deControl of Covalent Bond Enables Efficient Magnetic CoolingXin Tang,* Yoshio Miura, Noriki Terada, Enda Xiao, Shintaro Kobayashi, Allan Döring,Terumasa Tadano, Andres Martin-Cid, Takuo Ohkochi, Shogo Kawaguchi,Yoshitaka Matsushita, Tadakatsu Ohkubo, Tetsuya Nakamura, Konstantin Skokov,Oliver Gutfleisch, Kazuhiro Hono, and Hossein Sepehri-AminMagnetic cooling, harnessing the temperature change in matter whenexposed to a magnetic field, presents an energy-efficient and climate-friendlyalternative to traditional vapor-compression refrigeration systems, with asignificantly lower global warming potential. The advancement of thistechnology would be accelerated if irreversible losses arising from hysteresisin magnetocaloric materials are minimized. Despite extensive efforts tomanipulate crystal lattice constants at the unit-cell level, mitigating hysteresisoften compromises cooling performance. Herein, we address this persistentchallenge by forming Sn(Ge)3−Sn(Ge)3 bonds within the unit cell of theGd5Ge4 compound. This approach enables an energetically favorable phasetransition, leading to the elimination of thermal hysteresis. Consequently, weachieve a synergistic improvement of two key magnetocaloric figures of merit:a larger magnetic entropy change and a twofold increase in the reversibleadiabatic temperature change (from 3.8 to 8 K) in the Gd5Sn2Ge2 compound.Such synergies can be extended over a wide temperature range of 40–160 K.This study demonstrates a paradigm shift in mastering hysteresis towardsimultaneously achieving exceptional magnetocaloric metrics and opens uppromising avenues for gas liquefaction applications in the longstandingpursuit of sustainable energy solutions.X. Tang, Y. Miura, N. Terada, E. Xiao, T. Tadano, A. Martin-Cid,Y. Matsushita, T. Ohkubo, T. Nakamura, K. Hono, H. Sepehri-AminNational Institute for Materials ScienceTsukuba 305-0047, JapanE-mail: Tang.Xin@nims.go.jpY.MiuraFaculty of Electrical Engineering andElectronicsKyoto Institute of TechnologyMatsugasaki, Sakyo-ku, Kyoto 606-8585, JapanS. Kobayashi, T.Ohkochi, S. Kawaguchi, T.OhkuboJapanSynchrotronRadiationResearch Institute1-1-1 Kouto, Sayo 679-5198, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/adma.202514295© 2025 The Author(s). Advanced Materials published by Wiley-VCHGmbH. This is an open access article under the terms of the CreativeCommons Attribution-NonCommercial-NoDerivs License, which permitsuse and distribution in any medium, provided the original work isproperly cited, the use is non-commercial and no modifications oradaptations are made.DOI: 10.1002/adma.2025142951. IntroductionThe drive toward a carbon-neutral society,prompted by the environmental impactof traditional energy-intensive vapor-compression cooling technologies,[1] man-dates the exploration of green alternativeswith zero carbon emissions. Solid-statecaloric refrigeration technologies,[2] in-cluding electrocaloric,[3] elastocaloric,[4]and magnetocaloric[5–8] cooling, havethus emerged as promising solutions.Among them, the higher cooling poten-tial of magnetocaloric refrigeration hasmade it a front-runner to replace conven-tional vapor-compression refrigerationtechnology.[9] Utilizing the magnetocaloriceffect (MCE), this technology exploits thedegree of freedom of magnetic dipolesin materials to induce an isothermalmagnetic entropy change (ΔSm) or adi-abatic temperature change (△Tad).[6,8]Despite its potential applications, thecommercial viability of magnetocaloricA. Döring, K. Skokov, O. GutfleischDepartment of Functional MaterialsInstitute of Materials ScienceTechnical University of Darmstadt Peter-Grünberg Str. 16, 64287Darmstadt, GermanyT. OhkochiLaboratory of Advanced Science and Technology for IndustryUniversity of HyogoAko, Hyogo, Kamigori 678-1205, JapanT. Nakamura, H. Sepehri-AminInternational Center for Synchrotron Radiation Innovation Smart (SRIS)Tohoku UniversitySendai 980-8577, JapanAdv. Mater. 2025, e14295 e14295 (1 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbHhttp://www.advmat.demailto:Tang.Xin@nims.go.jphttps://doi.org/10.1002/adma.202514295http://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadma.202514295&domain=pdf&date_stamp=2025-12-17www.advancedsciencenews.com www.advmat.derefrigeration is hampered by the scarcity of high-performancemagnetic refrigerants.The discovery of a giant MCE (GMCE) in Gd5(Ge,Si)4 com-pound marked a major milestone,[10] and triggered extensivesearch for GMCEs in various intermetallic compounds, such as(Mn,Fe)2P,[11] MnAs,[12] the Ni-Mn-basedHeusler compounds,[5]and La(Fe,Si)13H.[13,14] These GMCEs arise from the nature ofthe first-order magnetic phase transitions (FOMTs). In FOMTmaterials, the magnetic and structural degrees of freedomare strongly coupled, resulting in latent heat and its associ-ated hysteresis. This introduces unwanted irreversibility andmechanical instability, making FOMT materials impracticalfor applications.[8,15,16] A conventional wisdom to mitigate thehysteresis is to weaken the magnetostructural phase transi-tion by tuning the crystallographic compatibility of two re-spective phases.[17–21] This is typically achieved by suppressingchanges in the symmetry or lattice constants of a unit cell.Despite numerous endeavors, this strategy has been plaguedby a persistent tradeoff: sacrificing a large MCE for a smallhysteresis. For instance, microalloying Fe in Gd5Ge2Si2 com-pound achieves minimal hysteresis by suppressing structuralchanges,[18] but this reduces −ΔSm from 18 to 7 J kg−1K−1. Hysteresis can be further reduced by tuning the natureof transition toward second-order magnetic phase transition(SOMT) in Si-rich Gd5(Ge1-xSix)4 compounds,[22] wherein fer-romagnetic ordering occurs without an alteration in the crystalstructure of Gd5Si4 compound,[23] enabling a reversible MCE;however, this reduces the giant value of –ΔSm to 6 J kg−1K−1. This tradeoff is commonly observed across many FOMTcompounds,[18,19,21,24–26] where the elimination of hysteresis of-ten diminishes the –ΔSm to one-half or one-third of its gi-ant value; outlining a formidable challenge in magnetic coolingtechnology.To address this challenge, we need to surpass the currentapproach. In the Gd5Ge4 compound, the magnetostructuralphase transition is governed by the interplay between the atomicfeatures of covalent bonds and magnetism. Specifically, thetransition from antiferromagnetic to ferromagnetic states in-volves a change in the covalent bond length of Ge3─Ge3 atinter-slab region within the unit cell from 3.62 to 2.62 Å fortwo respective orthorhombic structures, leading to hysteresisand irreversible functionality[27,28] (Figure 1a). Thus, control-ling the covalency at inter-slab region to weaken the magne-tostructural phase transition could effectively eliminate hys-teresis, while also utilizing the structure transition for GMCE.This necessitates nuanced control at the sub-unit-cell-level toexplore macroscopic properties. Herein, we employed chem-ical engineering to tailor the covalency within unit cell inan FOMT Gd5Ge4 compound (Figure 1b). As proof of con-cept, we have shown the formation of Sn(Ge)3−Sn(Ge)3 co-valent bonds within the unit cell of Gd5Ge4 compound en-ables an excellent combination of a large MCE and the elim-ination of hysteresis, which represents a paradigm shift inthe search for efficient magnetic refrigeration. These find-ings open transformative avenues for the rational design ofnext-generation magnetic refrigerants, particularly for practi-cal applications in liquefaction of gases such as H2, N2, andnatural gas, providing a green solution for efficient coolingtechnologies.2. Results and Discussion2.1. Approaching Hysteresis-Free TransitionThe Gd5Ge4 compound undergoes a magnetostructural phasetransition at 39 K under an external field of 2 T (Figure 2a),resulting in a GMCE in magnetic entropy change (ΔSm).[27,28]However, unlike ΔSm, adiabatic temperature change (ΔTad)—the equally important critical parameter for efficient MCE perfor-mance is underreported due to experimental challenges. In par-ticular, direct measurements of ΔTad under cyclic conditions re-main scarce, despite being essential for assessing the reversibilityof MCE. In this work, we directly and cyclically measuredΔTad torigorously assess MCE reversibility in Gd5Ge4 compound. Uponinitial application of a 5 T magnetic field, the compound ex-hibits aΔTad of 7 K associated with its first-order phase transition(Figure 2b). However, the large cooling effect is not sustained inthe subsequent cycles because of thermal hysteresis of approxi-mately 5 K (Figure 2a). Practically, only a ΔTad of 3.8 K can bemaintained. This phenomenon poses a challenge for all magne-tocaloricmaterials undergoing FOMT,[7,29,30] thus hindering theirpractical applications. The large thermal hysteresis observed inthe Gd5Ge4 compound arises from the interplay between cova-lent bonding at the sub-unit cell scale and magnetism.[27,28] Toaddress this issue, sub-unit cell-level engineering is required,and chemical substitution presents a potential solution. In thisstudy, we demonstrate this by substituting Ge with Sn in theGd5Ge4 compound. As shown in Figure 2a, a hysteresis-free tan-sition can be achieved in the Gd5Sn2Ge2 compound; the MCE inΔTad and -ΔSm are simultaneously improved to 8 K and 32 J kg−1K−1 (Figure 2b,d), respectively. A comprehensive understandingof the MCE enhancement by Sn substitution will require com-bined theoretical modeling and experiments that probe lattice vi-brations (phonons), spin excitations (magnons) and their inter-actions. Notably, the GMCE in ΔTad robustly withstands cyclicoperation via elimination of hysteresis (Figure 2b). It should beemphasized that the elimination of hysteresis in this work doesnot compromise the GMCE that is typically observed in FOMTmaterials, presenting a rare combination of benefits. The mag-netic hysteresis is further quantified as the enclosed area betweenthe ascending and descending magnetization curves after cool-ing from room temperature (shaded area in Figure 2c), repre-senting the energy lost as dissipated heat in a magnetic refriger-ation cycle.[24,31] The developed Gd5Sn2Ge2 compound exhibits anegligible hysteresis loss of 9 J kg−1, which is only one-sixth ofthe loss observed for Gd5Ge4 compound (55 J kg−1 at 39 K). Inaddition, we found this small hysteresis loss reproducible uponcylces (Figure S2, Supporting Information). This highlights thesignificant advantage of hysteresis elimination. While the end-member Gd5Sn4 compound[32] demonstrates a large −ΔSm, itsΔTad and cyclic stability remain unexplored, likely due to its airsensitivity. Similarly, Sn substitution in the Gd5(Ge,Si)4 systemis known to enhance MCE in –ΔSm and reduce hysteresis[33–35];however, its reversibility under cyclic conditions and the under-lying mechanisms remains poorly understood, partly due to thecompositional complexity, which complicates theoretical model-ing of local chemical effects on macroscopic behavior. Uncover-ing this hidden mechanism could unlock new strategies for de-signing materials that combine both giant and reversible MCEs.Adv. Mater. 2025, e14295 e14295 (2 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmat.dewww.advancedsciencenews.com www.advmat.deFigure 1. Strategy for achieving giant and reversible magnetocaloric effect (MCE). a) Limitation of first-order magnetic phase transition (FOMT): TheGd5Ge4 compound undergoes FOMT, transitioning from an antiferromagnetic to a ferromagnetic state, involving a transition between two orthorhombicstructures with different lattice constants. This transition results in a giant magnetocaloric effect (MCE) in an adiabatic temperature change (ΔTad)observed in thermometers. However, the giant MCE cannot be maintained in cyclic operation owing to large thermal hysteresis. b) Achieving giant andreversible MCE via covalent bond engineering: This approach involves compositional modifications in covalent bonds within a unit cell. For example,Adv. Mater. 2025, e14295 e14295 (3 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmat.dewww.advancedsciencenews.com www.advmat.deIn contrast, the Gd5Sn2Ge2 compound developed in this workprovides a chemically well-defined platform, enabling accurateinvestigation of how sub-nanoscale chemical modifications in-fluence reversibility of MCE.2.2. Deciphering the Phase TransitionHere, we investigated the structural details at the unit-cell andsub-unit-cell scales and examined their responses to externalstimuli. The Gd5Ge4-based compound, with an orthorhombicstructure (Pnma) (Figure 3a), consists of a layered architecture(slab) interconnected by Ge3─Ge3 covalent bonds.[22,28] Real-space imaging and spectroscopy via transmission electron mi-croscopy allow for the direct observation of these structures at theatomic scale. Figure 3a shows an element-resolved map reveal-ing Sn substitution for Ge within both the intra-slab and inter-slab regions. In the inter-slab region, the Sn atoms are resolvedand we use the notation Sn(Ge)3−Sn(Ge)3 to represent an aver-aged bond description, encompassing Ge3─Ge3, Sn3─Sn3, andGe3─Sn3 bonds within the inter-slab region of the Gd5Sn2Ge2compound. This leads to changes in both the lattice constant andbond length between the two slabs in the orthorhombic crystalstructure, as refined through synchrotron X-ray diffraction (S-XRD) patterns (Note S1, Supporting Information). Temperature-dependent S-XRD was then used to trace the thermally inducedphase transitions in detail. It’s noteworthy that the Gd5Ge4 com-pound exhibits a unique phenomenon, known as a kinetically ar-rested transformation (Figure S3, Supporting Information). Thisrequires an additional external field of 2 T to induce structuralchange.[28] Instead, a trace substitution of Si for Ge does not al-ter the strong characteristics of the FOMT,[22] as a similar ther-mal hysteresis of 5 K was recorded for Gd5Ge3.6Si0.4 compound,but enables a field-free phase transition driven solely by temper-ature changes (Figure S4, Supporting Information). Such con-sistency allows for the exploration of field-free thermally drivenphase transitions to understand the underlying mechanism ofhysteresis elimination in the Gd5Sn2Ge2 compound comparedto the Gd5Ge3.6Si0.4 compound.Figure 3b compares the in situ S-XRD measurements ofGd5Ge3.6Si0.4 and Gd5Sn2Ge2 compounds, showing distinct dis-tortions near the transition temperatures owing to a struc-tural transition between the two orthorhombic polymorphs inboth samples. The shift in the characteristic diffraction plane(Figure 3b) indicates a change in the lattice spacing of the unitcell (Figure 3c). During the cooling process, the high-temperatureorthorhombic (O(II)) phase transforms into the low-temperatureorthorhombic (O(I)) phase with a shear displacement along thea-axis,[28] resulting in approximately 2% shrinkage of the latticeconstant, a, for the Gd5Ge3.6Si0.4 compound. The change in ais more pronounced than those in the b and c lattice constants(Figure S5, Supporting Information). In contrast, the Gd5Sn2Ge2compound exhibits a smaller change in lattice spacing and unitcell volume during the transition. The shear displacement duringthe phase transition is further characterized by a change in thelength of the Ge3─Ge3 covalent bond in the Gd5Ge4-based sys-tem. For theGd5Ge3.6Si0.4 compound, the bond length (l) changesfrom 3.6 Å for the O(II) phase to 2.7 Å for the O(I) phase, whichis consistent with that observed for the Gd5Ge4 compound inthe transition process driven by a magnetic field.[28] In contrast,the formation of Sn(Ge)3─Sn(Ge)3 bonds in the Gd5Sn2Ge2 com-pound resulted in a small change of 0.3 Å in l. The presence oflatent heat is another signature of first-order phase transition, ev-idenced by the time evolution of the sample temperature near thetransition temperature (Figure 3d). For the two studied samples,the temperature rise during the initial run (1st run) was substan-tially suppressed due to the existence of latent heat, comparedto subsequent runs (2nd and 3rd runs). However, the degree ofsuppression in the 1st run for Gd5Sn2Ge2 compound was signifi-cantly lower than that observed for the Gd5Ge3.6Si0.4 sample. Thisindicates that the chemical substitution of Sn for Ge can sub-stantially weaken the nature of first-order phase transition. Con-sequently, our combined analysis of S-XRD and latent heat mea-surements confirmed that structural change and its associated la-tent heat were suppressed (but not completely eliminated) in theGd5Sn2Ge2 sample. This suppression was sufficient to eliminatehysteresis, resulting in a nonhysteretic transitionwhilemaintain-ing structural change for a GMCE. It should be noted further sub-stitution of Si for Ge in the Gd5Sn2Ge0.8Si1.2 compound elimi-nates latent heat (Figure S6, Supporting Information), leading toa smaller −ΔSm of 18 J kg−1 K−1.2.3. Mechanism of Thermomagnetic Phase TransitionsTo investigate the role of structural intricacies in controllingmag-netism and magnetostructural phase transitions, we conductedfirst-principles calculations. In the context of Landau theory,[36,37]the FOMT theoretically hinges on the energy barriers that sep-arate the local and global minima in the Gibbs free energy. ForGd5Sn2Ge2 compound, we resolved the phase transition betweenthe two polymorphs, resulting in changes in the unit-cell volumeand covalent bond lengths within the unit cell (Figure 3c). Here,we examined the influence of two potential factors—volume andshear displacement between Sn(Ge)3─Sn(Ge)3 bonds—on in-ducing the phase transition with different magnetic configura-tions. The observed lowest energies of the O(I) ferromagnetic(FM) phase at every volume (Figure 4a) indicate that the phasetransition cannot be attributed to volume changes alone. In con-trast, the shear displacement of the Sn(Ge)3─Sn(Ge)3 bond couldtrigger the phase transition (Figure 4a), as evidenced by two lo-cal energy minima for the O(II) antiferromagnetic (AFM) andin the Gd5Sn2Ge2 compound, the composition of covalent bonds changes from Ge─Ge to Sn(Ge)─Sn(Ge) bonds. The change in crystal structureupon transition is depicted using a unit cell with blue and red boxes representing two orthorhombic phases. Gd atoms in two orthorhombic structuresare denoted by green and blue spheres, with white arrows indicating their magnetic moments. Ge and Sn(Ge) atoms are represented by yellow andpink spheres, respectively, connected by black covalent bonds. The Gd5Sn2Ge2 compound is alloyed, with Sn atoms randomly distributed throughoutthe structure, including both inter-slab and intra-slab regions. Thus, the Sn(Ge)─Sn(Ge) bond description represents an average over Ge─Ge, Sn─Sn,and Ge─Sn bonds in the inter-slab region. For simplicity, only Ge3 and Sn(Ge)3 atoms are shown in the figure, this schematic is applicable to bothsingle-crystal and polycrystalline specimens and all measurements in this work were performed on polycrystalline samples.Adv. Mater. 2025, e14295 e14295 (4 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmat.dewww.advancedsciencenews.com www.advmat.deFigure 2. Advanced magnetocaloric effects (MCEs) in the Gd5Sn2Ge2 compound. a) Magnetization (M) is plotted versus temperature at an appliedmagnetic field of 2 T. b) Adiabatic temperature change (△Tad) of Gd5Ge4 compound (upper panel) shows a giant MCE in △Tad, which cannot bemaintained in cyclic fields. In contrast, we achieve a giant and reversible MCE in the Gd5Sn2Ge2 compound (lower panel of b). c) Energy loss caused byhysteresis for Gd5Ge4 and Gd5Sn2Ge2 compounds, which is numerically calculated using the enclosed area measured byMH (first loop) after coolingfrom room temperature. d) −∆Sm under a magnetic field change of 2 and 5 T measured for Gd5Ge4 and Gd5Sn2Ge2 compounds using multiple M–T curves and the Maxwell relation. The adiabatic temperature change was directly measured under adiabatic conditions by a thermometer, which isconfirmed via indirect measurement in Figure S1 (Supporting Information).O(I) FM phases observed at approximately ∆xi/a = 0 and −0.04(approximately shear displacement of −0.31 Å along a axis withrespect to the minima of O(I) FM phase), respectively. The cor-responding Sn(Ge)3─Sn(Ge)3 bond lengths are determined tobe 3.59 and 2.96 Å for O(II) AFM and O(I) FM phases, respec-tively, which agree with our experimental results (Tables S1 andS2, Supporting Information). To further understand the influ-ence of chemical composition on the magnetostructural phasetransitions, we studied this system for different compositions.In all studied compounds, the phase transition from O(I) FM toO(II) AFM is observed and associated with the shear displace-ment of covalent bonds (Figure S7, Supporting Information); thechange in bond length during the phase transition is smallerfor the Gd5Sn2Ge2 compound (Figure S8, Supporting Informa-tion). This calculation replicated experimental observations. In-terestingly, the activation barrier (△E), defined as the differencebetween the maximum energy along the transformation pathfrom O(I) FM to O(II) AFM and the initial energy (O(I) FM),reduce from 0.47 for Gd5Ge4 compound to 0.27 eV cell−1 forthe Gd5Sn2Ge2 compound (Figure 4b), indicating an energeti-cally more commensurate phase transition for Gd5Sn2Ge2 com-pound. This elucidates the elimination of hysteresis presentedin this work. Further investigation reveals that the Sn concentra-tion in the Sn(Ge)3─Sn(Ge)3 bonds within the inter-slab regionsignificantly influences both the activation energy and the mag-netostructural phase transition behavior (Note S2, SupportingInformation).To elucidate how Sn substitution in Gd5Ge4 reduces activa-tion energy, we analyzed the bonding nature using crystal or-bital Hamilton population (COHP) calculations. Experimentally,changes in the bond length at the inter-slab region were expectedto influence the 8d-site Gd-X3 (X = Ge, Si, Sn) bonds and theircovalency due to hybridization between the d orbitals of Gd andp orbitals of X3. COHP calculations of the Gd−X3 bonds areshown in Figure 4d. The bond strength (covalency) can be eval-uated by the integration of the COHP with an energy range of−4.0 eV to Fermi energy. Integration of the ─COHP (─ICOHP)for the O(I) FM structure reveals that the Gd─Sn bond has asmaller ─ICOHP of 0.339 (0.349) for majority (minority)-spinstates, compared to 0.402 (0.426) for the Gd─Ge bond and 0.417(0.441) for the Gd-Si bond. Similar results are obtained for theO(II) AFM structure (Figure S9, Supporting Information). Theseresults suggest that Sn doping reduces covalency of Gd─X atinter-slab region in Gd5Ge4 compound, possibly due to the spa-tial broadening of the Sn─5p wavefunction relative to the Ge-4pwavefunction. Structural changes are also anticipated to affectthe local density of states (LDOS) of the studied compounds. Asshown in Figure 4e,f, the LDOS of the 8d-site Gd-d andGe(Sn,Si)-p states in the O(I) FM phase of Gd5Ge2Sn2 shifts to higher ener-gies compared to those inGd5Ge4 andGd5Ge3.6Si0.4 compounds.Adv. Mater. 2025, e14295 e14295 (5 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmat.dewww.advancedsciencenews.com www.advmat.deFigure 3. Characterization of atomic features at and within unit-cell scales and their response to external stimuli. a) Crystal structure of a unit cell andbonds within a unit cell characterized via transmission electron microscopy. A unit cell of pnma crystal structure is depicted for Gd5Ge4 compound,with red spheres representing Gd atoms and green spheres representing Ge atoms. Ge occupies three nonequivalent sites: Ge1 (light green spheres)and Ge2 (light green spheres) are located within the slab, while Ge3 (dark green spheres) is situated in the inter-slab region, with the Ge3─Ge3 bondconnecting two slabs, bond length l. High-resolution high-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) imageacquired along the [101] projection, with superimposed crystal structure (only showing Ge atom for simplicity) and energy-dispersive X-ray spectroscopy(EDS) maps showing the distributions of Gd and Sn in the Gd5Sn2Ge2 compound, this indicates that Sn replaces Ge at both intra-slab (Ge1, Ge2) andinter-slab (Ge3) regions. Atomic arrangement within the inter-slab region of the Gd5Sn2Ge2 compound from crystal structure and determined from EDSanalysis focused on inter-slab area for constituent elements, Gd (red), Sn (blue) and Ge (green). b) Temperature-dependent synchrotron X-ray diffraction(S-XRD) patterns are presented for Gd5Ge3.6Si0.4 (upper panel) and Gd5Sn2Ge2 (lower panel), with the black dashed line illustrating the characteristicdiffraction plane shift during the phase transition. c) Temperature-dependence of the lattice parameters (a, volume (v) of a unit cell) and bond length lare obtained from the Rietveld refinement of S-XRD data. The x-axis represents the temperature minus transition temperature (Ttr). d) Time evolution ofthe sample temperature obtained using the relaxation method at the transition temperature for Gd5Ge3.6Si0.4 and Gd5Sn2Ge2 compounds. The dashedlines denote heat power for each measurement (1st (black), 2nd (blue) and 3rd (red) measurements).The bonding state at around energy level of −1.3 eV shift tohigher energy also confirms the weaker covalency in Gd5Sn2Ge2compound. Similar energy shifts are also observed in the AFMstate (Figure S10, Supporting Information). These changes in co-valency are expected to further influence exchange interactions.We then calculated the energy difference between the FM andAFM states (∆E = EFM − EAFM) to quantify the exchange interac-tion. For Gd5Ge4 compound, the exchange interaction energiesfor the O(I) and O(II) structures are −0.45 and 0.24 eV cell−1, re-spectively (Figure 4g). The exchange energy is further illustratedby positioning the energies of O(I) AFM and O(II) FM withinthe energy landscape in Figure 4b, which shows that the energyprofile can be strongly influenced by exchange interactions. WithSn substitution, the magnitude of exchange interaction energydecreases by 0.07 eV cell−1, from −0.45 to −0.38 eV cell−1 forthe O(I) structure, and 0.11 eV cell−1, from 0.24 to 0.13 eV cell−1for the O(II) structure (Figure 4g). This exchange interaction re-duction can explain the overall reduction in activation energy,which decreases from 0.47 to 0.27 eV cell−1 due to Sn substitution(Figure 4b).We further examined exchange interaction constants (Jij)within (intra-slab) and between neighboring slabs (inter-slab) forthe 20 Gd atoms in the unit cell (Figure 4c) using SPR-KKR code,with pairwise Jij data detailed in Table S3 (Supporting Informa-tion). Figure 4h compares the difference of pairwise exchangeinteractions between Gd5Ge4 and Gd5Sn2Ge2 compounds, indi-cating that interactions are generally stronger in Gd5Ge4 com-pound, agreeing with calculations using density functional the-ory (DFT) (Figure 4g). The Sn substitution significantly impactsGd3-Gd7 and Gd3-Gd6 pairs, connecting Gd atoms across slabs.This highlights the importance of chemical engineering in theinter-slab region. The exchange interaction difference estimatedusing Jij, between the relaxed O(I) FM phase and O(II) AFMphase shows a reduction from 0.374 eV cell−1 in the Gd5Ge4compound to 0.291 eV cell−1 in the Gd5Sn2Ge2 compound, in-dependently verifying that Sn alloying weakens exchange inter-actions and reduces activation energy. We then explored how theinter-slab exchange interactions influence the AFM-to-FM tran-sition. As depicted in Figure 4i, the inter-slab Gd3-Gd7 and Gd3-Gd8 pairs exhibit largest change in Jij between O(II) AFM andAdv. Mater. 2025, e14295 e14295 (6 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmat.dewww.advancedsciencenews.com www.advmat.deFigure 4. First principles calculations revealing the role of covalent bonds within a unit cell in shaping the magneto-structural phase transition andmagnetism. a) Relative energy as a function of volume, with fixed atomic positions for each structure and relative energy as a function of shear dis-placement of neighboring slabs, with the shear displacement along a-axis in fractional coordinates ∆xi/a, while the volumes are fixed for each structure.We consider the two structures, O(I) and O(II), each with two different magnetic configurations: ferromagnetic (FM) and antiferromagnetic (AFM).The relative energy is the energy with respect to energy minimum of the O(I) FM phase, In the lower panel, we set the minimum of the O(I) ferro-magnetic structure as 0 for x-axis. b) Energy relative to the energy minimum of the O(I) FM phase as a function of shear displacement along a-axis infractional coordinates ∆xi/a, for Gd5Ge4, Gd5Ge3.6Si0.4 and Gd5Sn2Ge2 compounds. We set the minimum of the O(I) ferromagnetic structure as 0 forx-axis in each studied compound. The activation barriers, △E, from the O(I) FM to O(II) AFM phases are determined to be 0.27 and 0.47 eV cell−1 forGd5Sn2Ge2 and Gd5Ge4 compounds, respectively, which are illustrated by solid red and green arrow. To examine the effect of exchange interaction, thepositions of O(II) FM (open squares) and O(I) AFM (solid spheres) for Gd5Ge4 (green) and Gd5Sn2Ge2 (red) compounds in the energy landscape arealso illustrated, the dashed lines denote the exchange interaction for O(I) and O(II) structures in Gd5Ge4 (green) and Gd5Sn2Ge2 (red) compounds.c) The unit cell of the Pnma crystal structure. Red spheres represent Gd atoms, while light and dark green spheres represent Ge atoms at the 4c-siteand 8d-site, respectively. The Ge3 sites, which occupy the 8d position, are located in the inter-slab region, whereas Ge1 and Ge2 occupy the 4c sites inthe intra-slab region. Gd atoms in the unit cell are labeled in the unit cell; for example, the eight Gd atoms at the inter-slab region are designated asGd1 through Gd8, the dash black square shows a slab within unit cell. d) Energy-dependent crystal orbital Hamilton population (COHP) of Gd–X (whereX = Ge, Si, Sn) at the 8d-site in the inter-slab region, the red-shaded area represent integration of the −COHP (−ICOHP) for Gd-Sn in Gd5Sn2Ge2compound and their −ICOHP values are listed in d. e) Energy-dependent local density of states (LDOS) for the 8d-site Gd-d orbitals in Gd5Ge4 (green),Gd5Ge3.6Si0.4 (blue), and Gd5Sn2Ge2 (red) at O(I) FM state. f) Energy-dependent LDOS for the 8d-site Ge-p orbital in Gd5Ge4 (green), (Ge,Si)-p orbitalin Gd5Ge3.6Si0.4 (blue), and (Sn,Ge)-p orbital in Gd5Sn2Ge2 (red) at O(I) FM state. Positive (negative) values on the vertical axis correspond to LDOS inthe majority (minority) spin states. Due to structural differences in these three compounds, the Gd s-core state is used as a reference to align the bandpositions, resulting in a 0.1368 eV shift to higher energy and 0.01652 eV shift to lower energy for Gd5Sn2Ge2 and Gd5Ge3.6Si0.4 compounds, respectively,compared to Gd5Ge4 compound. The dashed line indicates the Fermi level for the Gd5Ge3.6Si0.4 (blue) and Gd5Sn2Ge2 (red) compounds. (Sn,Ge) andAdv. Mater. 2025, e14295 e14295 (7 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmat.dewww.advancedsciencenews.com www.advmat.deO(I) FM states. During the phase transition process, the ther-mally driven displacement of inter-slab Ge(Sn) atoms modulatesinter-slab interactions as indicated by the spin density contourmap (Figure 4j). This modulation drives the magnetism transi-tion from AFM to FM state as shown by theoretical density ofstates (Figure S11, Supporting Information) and experimentallymeasured Gd moment using XMCD (Note S3, Supporting In-formation). These theoretical insights highlight the critical roleof inter-slab bonds in controlling magnetostructural and mag-netism transitions.2.4. Applicability of Developed MaterialsAnother challenge in implementing magnetic cooling systems isthe limited operating temperature range of the refrigerants, pri-marily because of the narrow temperature span of the GMCE.A solution to this constraint—based on active regenerationschemes—necessitates the tunability of the transition tempera-ture inmagnetocaloric materials. A broad transition temperaturerange of 40–160 K can be achieved by strategically substitutingDyfor Gd and Si for Ge (Figure 5a). Furthermore, −ΔSm above 18 Jkg−1 K−1 (Figure 5b) is maintained for these nonhysteretic tran-sitions andΔTad for all developed compounds remains stable un-der cyclic operation (Figure S12, Supporting Information). Next,we evaluated the superiorities of magnetocaloric performanceacross two crucial dimensions (ΔTad, −ΔSm) as preferred by ap-plication and compared them with those of widely investigatedrefrigerants. The compounds developed herein exhibited an ex-cellent combination of these favorable properties. Figure 5c,dshows the reversible MCEs at 15–160 K for a wide range ofmaterials.[21,32,38–57] The absence of materials with a large MCEfor both ΔTad and −ΔSm above 50 K represents a material bottle-neck for cryogenic applications in magnetic refrigeration tech-nology. This challenge can be addressed by implementing thedeveloped materials into a magnetic cooling system for gas liq-uefaction, as they exhibit giant MCEs in both −ΔSm and re-versible ΔTad. Among these, the Gd5Sn2Ge2-based compoundsexhibited 1.5–2 times larger MCEs than most existing magneticrefrigerants in both ΔTad and −ΔSm. Although the Gd5Sn4 com-pound shows a large MCE around 90 K, its hysteresis behav-ior and associated reversibility under cyclic conditions have notyet been reported.[32] Similarly, Eu2In shows a larger −ΔSm at59 K, but the air-sensitive nature of both Gd5Sn4 and Eu2Incompounds[32,57]undermines their applicability. In contrast, thedeveloped Gd5Sn2Ge2 compound demonstrates good phase sta-bility under air exposure (Figure S13, Supporting Information).To further evaluate the properties, we consider another magne-tocaloric metric, refrigeration capacity (RC) shown in Note S4(Supporting Information). A −ΔSm−RC diagram encompassesa diverse family of materials with transition temperatures span-ning from 15 to 320 K. The effective RCs for FOMT materi-als are confined to values below 400 J kg−1, falling short of theachievements of thematerials developed here. Conversely, SOMTmaterials have higher RC values, but their magnetocaloric per-formance is overshadowed by their lower values of −ΔSm. TheGd5Sn2Ge2 compounds in our work exhibit a unique combina-tion of large effective RC of 550 J kg−1 and−ΔSm of 32 J kg−1 K−1.In addition, the developed Gd5Sn2Ge2 compound exhibit goodmechanical stability during the cyclic operation and attractivecost performance (Note S5, Supporting Information). These com-parisons underscore the potential of the developed compoundsfor the magnetic liquefaction of gases (H2, N2, natural gas) andtheir complementarity to Gd-based materials[58–61] operating be-low 10 K—advancing the development of high-performance cryo-genic refrigerants.3. Summary and OutlookIn conclusion, we propose and demonstrate a novel approach tomitigate hysteresis in FOMT materials without sacrificing theirmagnetocaloric effect. The conventional approach is to achieve acrystallographically compatible phase transition bymanipulatingthe overall unit cell properties. However, this method often facesa persistent trade-off between a giant MCE and good reversibil-ity. Our approach involves precise control at the sub-unit-cellscale by the formation of Sn(Ge)3─Sn(Ge)3 bonds in the Gd5Ge4-based compound. This strategy promotes a favorable energy land-scape for the magnetostructural phase transition by weakeningof exchange interaction, unlocking the potential of FOMT mag-netocaloric materials without introducing hysteresis-associatedside effects. This delivers a synergistic achievement of magne-tocaloric metrics. Moreover, the versatility of applications for thedeveloped compounds has been demonstrated by their tunable,nonhysteretic phase transitions. A comprehensive evaluation ofprimary magnetocaloric properties establishes that the materialsdeveloped in this study hold significant promise for applicationsacross a spectrum of magnetic refrigeration materials, particu-larly in the search of green alternative for gas liquefaction.(Ge,Si) denote the Sn/Ge and Ge/Si mixtures, respectively, based on their compositions. g) Exchange interaction energy (ΔE = EFM − EAFM) betweenthe ferromagnetic (FM) and antiferromagnetic (AFM) states across calculation steps transitioning from the O(II) structure to the O(I) structure, withvarying shear displacement,∆xi/a. Since the shear displacement for two compounds is different, the top x-axis and bottom x-axis corresponds to Gd5Ge4and Gd5Sn2Ge2 compounds, respectively. We set the O(I) FM structure as 0 for x axis. h) Pairwise comparison of exchange interactions in Gd5Ge4 andGd5Sn2Ge2 compounds, ∆Jij = Jij(Gd5Ge4) − Jij(Gd5Sn2Ge2), the difference of pairwise Jij between Gd5Ge4 and Gd5Sn2Ge2 compounds. “Gd3-Gd7”refers to the pair interaction between atoms Gd3 and Gd7 as shown in c. Equivalent pairs, such as pairs Gd1-Gd5, Gd13-Gd17, and Gd15-Gd19, sharethe same pair distance and exchange interaction constant (Jij) with Gd3-Gd7 due to periodicity and local symmetry (Table S3, Supporting Information).The x-axis indicates the pair distance in the Gd5Ge4 compound. i) Pairwise comparison of difference in exchange interactions between the O(I) FMand O(II) AFM states in the Gd5Ge4 and Gd5Sn2Ge2 compounds, with the x-axis showing the pair distance in FM state of Gd5Ge4 and Gd5Sn2Ge2compounds. The open circles stand for difference of intra-slab interaction and solid circles represent difference of inter-slab interaction. j) Spin densityfor the O(II) AFM and O(I) FM phases for the Gd5Sn2Ge2 compound is depicted with a cut at z = c/2 of the crystallographic structure. The positions ofintra-slab Gd and inter-slab Sn(Ge)3 are labeled as Gd and Ge3, respectively, in the spin density map. In the O(II) AFM state, two intra-slab Gd exhibitantiferromagnetic coupling, whereas in the O(I) FM state, they show ferromagnetic coupling. The two Sn(Ge)3 atoms are isolated at the O(II) AFMstate, indicative of broken bonds, while they are connected in the O(I) FM state.Adv. Mater. 2025, e14295 e14295 (8 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmat.dewww.advancedsciencenews.com www.advmat.deFigure 5. Versatile application for gas liquefaction by tailoring transition and comparingMCEs with those of widely researchedmagnetocaloric materials.a) Temperature-dependent magnetizationM(T) measurements of the cooling and heating branches at 1 K intervals (μ0H = 2 T) for a series of magneticrefrigerants with tailored transition temperatures, covering the temperature window required for application of H2, N2, and natural gas (NG) liquefaction.b) Temperature-dependent magnetic entropy change −ΔSm(T) curves of magnetic refrigerants under a field change of 2 T (open circle) and 5 T (solidcircle). The colors of the curves in a, b correspond to the color of the listed alloy compositions in a. c) Comparison of reversible adiabatic temperaturechange (ΔTad) at the field change of 5 T is made with other magnetocaloric materials with transition temperature from 15 to 170 K. Indirect measurementofΔTad for HoB2,[38] Ho5Si4,[39] Tb5Ge2Si2,[40] (Dy,Tb)FeSi,[48] Gd5Sn2Ge2 compound (open red circle) and direct measurement for rare earth (RE)Al2,RENi2,[41,42] (Er,Ho)(Co,M)2,[21] and Gd5Sn2(GeSi)2 compounds (3D red spheres) of this study. d) Comparison of magnetic entropy change undera field change of 5 T for the developed compounds with other magnetocaloric materials with nonhysteretic transitions ranging from 15 to 170 K. The−ΔSm for Gd5Sn4,[32] REB2,[38,43] REGa,[44,45] GdNi2,[41] Ho(Ni,Co)2,[46] REAl2,[41] REN,[47] (Dy,Tb)FeSi,[48] GdNiCo,[49] (Er,Ho)(Co,M)2,[21] RE3Al2,[50]RE5Si4,[39,40] RE3CoNi,[51] RE2In,[52–55] Gd5Ge3Sb1,[56] Eu2In,[57] and Gd5Sn2(GeSi)2 compounds of this study.4. Experimental SectionMaterials Preparation and Thermomagnetic Measurements: Polycrys-talline Gd5Ge4-based samples were synthesized via the arcmelting of pureconstituent elements in an Ar atmosphere, incorporating 0.5–5 wt% ad-ditional rare earth to compensate for evaporation losses during samplepreparation. The ingots were remelted four times after flipping to ensurehomogeneity. A thermomagnetic analysis was performed using a super-conducting quantum interference device magnetometer (SQUID-VSM).Temperature-dependent magnetization (M(T)) measurements were con-ducted on both the cooling and heating branches at 1-K intervals. Thetemperature-dependent magnetic entropy change (−ΔSm(T)) was calcu-lated based on the following Maxwell’s relation from multipleM–T curvesat various external fields:ΔSm = 𝜇00∫H(𝜕M𝜕T)HdH (1)DirectMeasurement of Adiabatic Temperature and LatentHeat: Tomea-sure the adiabatic temperature change directly, a thermometermade of zir-conium oxynitride thin-film Cernox (CX-SD, Lake Shore Cryotronics) wasplaced on the large surface of an approximately cubic sample and fixedby thin copper plates and thin copper wires. The background adiabatictemperature change contributed from the sample holder was subtractedconsidering its heat capacity. The sample assembly was inserted into aquantum design physical property measurement system (PPMS) manu-factured by the QuantumDesign Company to control the temperature andmagnetic field. The sample space was pumped to obtain adiabatic condi-tions using a cryopump, and the pressure wasmaintained below 10−4 Torr.For latent heat measurements, the relaxation method implemented in thePPMSwas employed. The latent heat was evaluated bymeasuring the timeevolution of the sample temperature during measurement using the relax-ation method. Details of this method are provided in Note S6 (SupportingInformation).IndirectMeasurement of Adiabatic Temperature: This property was stip-ulated after performing heat capacity measurements in the Quantum de-sign PPMS. Heat capacity was measured in a plate-shaped sample usingthe 2𝜏 method in applied magnetic fields of 0 and 5 T. The following equa-tion allows to calculate entropy as a function of temperature in differentmagnetic fields:S (T,H) =T∫0(CPT)HdT (2)The indirect ΔTad is obtained considering an isoentropic difference ofS(T,H0) and S(T,Hf), where H0 denotes the entropy curve for 0 T applied,andHf refers to the entropy with an applied field different than 0 T, as givenin the following equation:ΔTad = T(S,Hf)− T (S,H0) (3)Adv. Mater. 2025, e14295 e14295 (9 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmat.dewww.advancedsciencenews.com www.advmat.deStructure Characterizations: The phase transition process was trackedusing an in situ synchrotron X-ray diffractometer (S-XRD) at the BL02B2beamline of SPring-8. The measurement samples were ground into finepowders, placed in a borosilicate glass capillary (diameter, 0.3 mm andsealed with He gas. The temperatures of the powder samples were con-trolled using He and N2 gas blowers. Temperature-dependent S-XRD pat-terns were collected during heating from 30 to 200 K. The samples wererotated during the measurements to improve the particle statistics. Six 1Dsolid-state (MYTHEN) detectors were used to collect the XRD patterns.Diffraction data from 2° to≈78°were acquired via XRDmeasurements us-ing multiple detectors at two designated detector angle positions (double-step measurements). The beam size was collimated to 0.5 mm (height) ×1.5 mm (width). The wavelength was determined to be 0.4956635 Å afterconducting the calibration using CeO2 standard sample. Scanning trans-mission electron microscopy (Spectra Ultra STEM, Thermo Fisher Scien-tific) equipped with energy-dispersive X-ray spectroscopy using four detec-tors was employed to observe the atomic-scale features. Drift correctionwas applied by the system during elemental mapping. The TEM sampleswere prepared using an FEI Helios G4-UX dual-beam system with the lift-out technique.Evolution of Element-Specific Moment: Soft X-ray magnetic circulardichroism (XMCD) measurements were performed using the BL25SUbeamline at the SPring-8 synchrotron radiation facility. The XMCD spec-tra at the Gd M4,5 edges were recorded at different temperatures duringheating from 40 K in the ferromagnetic state to 160 K. A degree of circu-lar polarization of 0.96 at 400 eV has been previously estimated[62] and isexpected to be similar in the energy region used in this work. The spec-tra were recorded using the total electron yield method, with an angle be-tween the incident X-ray beam and the magnetic field of 10 degrees.[63]Samples were prepared in a rod shape with a 1 mm2 square section and10 mm length and fractured in the ultra-high vacuum chamber of theXMCD system with a vacuum level of < 5 × 10−7Pa, allowing the mea-surement of the fresh surface. The XMCD signal (μXMCD) was obtainedas μXMCD = (μl − + μr +) − (μl + + μr −) where μl and μr represent theX-ray absorption spectrum (XAS) for the “left-handed” (h−) and “right-handed” (h+) helicity, respectively, and μ+ and μ− represent the XAS forthe positive and negative external appliedmagnetic field of 1.9 T.Magneto-optical sum rule analysis for XMCD[64–66]was used to calculate the mag-netic moments of Gd, considering the spin correction factor for rareearths.[67]First-Principles Calculations: Spin-polarized DFT calculations were per-formed using the projected augmented wave pseudopotential method asimplemented in the Vienna Ab initio Simulation Package code.[68] Theexchange-correlation interaction was approximated using the Perdew–Burke–Ernzerhof[69] formulation based on the generalized gradient ap-proximation (GGA). K-point sampling of the Brillouin zone was performedusing a 6 × 3 × 6 k-mesh grid. The spin-orbit coupling (SOC) was not con-sistently included in the calculations. The localized 4f electrons of Gd weretreated based on the implementation of Hubbard’sU parameter using theDFT + Umethod with U = 6.7 eV and J = 0.7 eV. The lattice constants andatomic positions of the O(I) and O(II) structures with FM and AFM stateswere determined by atomic relaxation in DFT calculations, and Sn and Sidoping in Gd5Ge4 was simulated using a virtual crystal approximation.[70]A correction of the Columb interaction was made by giving an on-site Uand J to the Gd f-orbital to obtain the correct Gd spin moment (7 μB).This has been done in previous studies[71] and considered to be one ofthe methods to treat the Gd f-orbital correctly in the DFT calculations. Thevalues of U and J that were used taken directly from the previous studies.Crystal Orbital Hamilton Population (COHP) analysis is conducted usingthe LOBSTER code.[72]Exchange interaction constants were computed using spin-polarizedrelativistic Korringa–Kohn–Rostoker (SPR-KKR) package,[73,74] with op-timized structures obtained by VASP. The k mesh for self-consistentand Jij calculations was chosen as 5 × 2 × 5 and 12 × 6 × 12, re-spectively. The exchange-correlation interaction was approximated us-ing the Perdew–Burke–Ernzerhof formulation.[69] Full-potential spin-polarized scalar-relativistic Korringa–Kohn–Rostoker method (FP-SP-SREL-KKR)[75]was employed that SOC was not included in the calculation.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThis study was in-part supported by the JSPS International Joint ResearchProgram (JRP-LEAD with DFG; program number JPJSJRP20221608), JSTERATO “Magnetic Thermal Management Materials” (Grant No. JPM-JER2201) and JSPS KAKENHI Grant Number JP19H05819 (to Y.M.),23H00183 (to T.T.), JSPS KAKENHI Grants No. 22H00297 (to N.T.). Syn-chrotron radiation experiments were performed at BL02B2 and BL25SU ofSPring-8 with the approval of the Japan Synchrotron Radiation Research In-stitute (JASRI) (Proposal Nos. 2023A1183, 2023A1510, and 2023A1730).H.S.-A. and T.N. acknowledge the support from the NIMS-TOHOKU JointResearch Partnership Program. O.G. and K.S. acknowledge financial sup-port by the Deutsche Forschungsgemeinschaft (DFG) within the CRC/TRR270 (Project-ID 405553726). A part of this work was supported by the Elec-tronMicroscopy Unit, National Institute forMaterials Science (NIMS).Thecalculations in this study were performed on the Numerical Materials Sim-ulator at National Institute for Materials Science (NIMS).Conflict of InterestThe authors declare no conflict of interest.Author ContributionsX.T. developed this idea and prepared the alloys. X.T. performed themagnetothermal measurements. N.T. performed adiabatic temperaturechanges and latent heat measurements. Y.M. conducted DFT calculationsand crystal orbital Hamilton population (COHP) analysis. E.X. and T.T.conducted the pairwise exchange interaction calculation using SPR-KKRcode. S.K. and X.T. carried out in situ synchrotron X-ray diffraction mea-surements and analyzed the data. T.O., X.T., A.M., and T. N. conducted softX-ray magnetic circular dichroism (XMCD) measurements and analyzedthe obtained XMCD spectra. X.T. conducted high-resolution transmissionelectronmicroscopy observations. A.D., K.S., andO.G. performed the indi-rect measurements of the adiabatic temperature change. Y.M. investigatedthe temperature dependence of the X-ray diffraction measurements. X.T.and H.S. interpreted key findings and wrote the manuscript. O.G., T.O.,K.H., and H.S. supervised the study. All the authors discussed the resultsand commented on the manuscript.Data Availability StatementThe data that support the findings of this study are available from the cor-responding author upon reasonable request.Keywordshysteresis, magnetic cooling, magnetocaloric materialsReceived: July 24, 2025Revised: October 30, 2025Published online:[1] UNEP, 2010 Report of the Refrigeration, Air Conditioning and HeatPumps Technical Options Committee (RTOC) Montreal protocol onsubstances that deplete the ozone layer, 2011.Adv. Mater. 2025, e14295 e14295 (10 of 12) © 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH 15214095, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202514295 by National Institute For, Wiley Online Library on [13/01/2026]. 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