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## Creator

[Ravi Gautam](https://orcid.org/0000-0002-5442-6328), [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), [Abdulkareem Alasli](https://orcid.org/0000-0002-1681-0492), Hosei Nagano, [Tadakatsu Ohkubo](https://orcid.org/0000-0003-3548-1951), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), [Hossein Sepehri-Amin](https://orcid.org/0000-0002-7856-7897)

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[Creation of flexible spin-caloritronic material with giant transverse thermoelectric conversion by nanostructure engineering](https://mdr.nims.go.jp/datasets/35e2609b-8160-43c4-861e-cc3e9883930d)

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Creation of flexible spin-caloritronic material with giant transverse thermoelectric conversion by nanostructure engineeringArticle https://doi.org/10.1038/s41467-024-46475-6Creationofflexible spin-caloritronicmaterialwith giant transverse thermoelectricconversion by nanostructure engineeringRavi Gautam1, Takamasa Hirai 1, Abdulkareem Alasli 2, Hosei Nagano2,Tadakatsu Ohkubo 1, Ken-ichi Uchida 1 & Hossein Sepehri-Amin 1Functional materials such as magnetic, thermoelectric, and battery materialshave been revolutionized through nanostructure engineering. However, spincaloritronics, an advancingfield basedon spintronics and thermoelectricswithfundamental physics studies, has focused only on uniform materials withoutcomplex microstructures. Here, we show how nanostructure engineeringenables transforming simple magnetic alloys into spin-caloritronic materialsdisplaying significantly large transverse thermoelectric conversion properties.The anomalous Nernst effect, a promising transverse thermoelectric phe-nomenon for energy harvesting and heat sensing, has been challenging toutilize due to the scarcity of materials with large anomalous Nernst coeffi-cients. We demonstrate a remarkable ~ 70% improvement in the anomalousNernst coefficients (reaching ~ 3.7 µVK−1) and a significant ~ 200%enhancementin the power factor (reaching ~ 7.7 µWm−1K−2) in flexible Fe-based amorphousmaterials by nanostructure engineering without changing their composition.This surpasses all reported amorphous alloys and is comparable to singlecrystals showing large anomalous Nernst effect. The enhancement is attrib-uted to Cu nano-clustering, facilitating efficient transverse thermoelectricconversion. This discovery advances the materials science of spin calori-tronics, opening new avenues for designing high-performance transversethermoelectric devices for practical applications.Thermoelectric devices have emerged as a promising technology forgenerating electricity by scavenging waste heat, representing a vitalstep towards achieving a more sustainable future1–3. These devicesleverage thermoelectric effects, enabling the direct interconversionbetween heat and electricity. Additionally, heat currents can alsointeract with spin-dependent transport, giving rise to the field of spin-caloritronics, which focuses on the interconversion of spin, charge,and heat currents3–5. However, current technology in this realm relieson a complexmodule structurebasedon the Seebeck effect, which hasinadequate thermal insulation4,6. To overcome this problem, researchinterest in transverse thermoelectric conversion such as theanomalous Nernst effect (ANE) has been raised3,5. ANE can convert atemperature gradient into anorthogonal voltage inmagneticmaterials(Fig. 1) and is the Onsager reciprocal of the anomalous Ettingshauseneffect (AEE)3,4,7–12. ANE is one of the hottest topics in spincaloritronics4,5,13 because it enables the design of thermoelectric devi-ces with a simple lateral structure, convenient scalability, and easyfabrication. Additionally, its transverse geometry facilitates efficientand flexible coverage of curved heat sources, making it ideal for har-vesting thermal energy from large-area heat sources. Compared toconventional Seebeck-effect-based devices, ANE-based devicesrequire fewer manufacturing processes, exhibit lower contactReceived: 10 October 2023Accepted: 28 February 2024Check for updates1National Institute for Materials Science, Tsukuba 305-0047, Japan. 2Department of Mechanical Systems Engineering, Nagoya University, Nagoya 464-8601,Japan. e-mail: uchida.kenichi@nims.go.jp; h.sepehriamin@nims.go.jpNature Communications |         (2024) 15:2184 11234567890():,;1234567890():,;http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-1681-0492http://orcid.org/0000-0002-1681-0492http://orcid.org/0000-0002-1681-0492http://orcid.org/0000-0002-1681-0492http://orcid.org/0000-0002-1681-0492http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-46475-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-46475-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-46475-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-46475-6&domain=pdfmailto:uchida.kenichi@nims.go.jpmailto:h.sepehriamin@nims.go.jpresistance, and may offer superior thermoelectric conversionperformance2,14. ThismakesANE apromisingpath for thedevelopmentof next-generation thermoelectric devices with potential applicationsranging from thermal management technologies to heat flux sensors2.However, further improvement of the thermopower of ANE is needed,which is the current bottleneck for its practical applications. As thedemand for modern devices continues to rise, achieving a significanttransverse thermoelectric response and understanding the underlyingmechanisms become crucial for optimizing efficiency and powergeneration capabilities. To accomplish this, a novel approach isrequired to design low-cost and flexible materials that exhibit largeANE, thereby advancing its use in cutting-edge thermoelectric devices.The discovery of remarkable ANE in magnetic topological mate-rials has triggered a surge of interest, and significant efforts have beendirected toward enhancing ANE through materials research. Forexample, several magnetic materials such as Heuslercompounds7–9,15–19, ferromagnetic binary alloys10,12,14,20–28, Weylantiferromagnet29–31, and permanent magnets11,32–34 have been exten-sively investigated. However, only a few of these materials have dis-played the anomalous Nernst coefficient SANE, transversethermopower due to ANE, surpassing 1 µVK−1, with Co-based Heusleralloys demonstrating particularly remarkable values of 6–8 µVK−1 atroom temperature8. Additionally, while most research has pre-dominantly focused on crystalline materials, there has been a recentemergence of studies exploring amorphous materials34–40. Iron (α-Fe)is known as the most abundant ferromagnetic element, but it exhibitstiny ANE10,12,22. Thus, it would be favorable to develop a versatile Fe-based bulk material with large ANE to obtain highly efficient thermo-electric devices. So far, particular emphasis has been directed onmaterial design anddevelopment to increase the ANE viamanipulatingthe Berry curvature near the Fermi level11,17,19,28,29. However, littleattention has beenpaid to howmicrostructureengineering at differentlength scales can influence the transport properties and ANE. This canpotentially unveil new strategies to enhance ANE, thus advancing ourunderstanding and application of this effect in thermoelectric andenergy conversion devices.In this study, we demonstrate how nanostructure engineering ofmagnetic materials can significantly improve the transverse thermo-electric conversion properties.We present a schematic representationof our strategies in Fig. 1. To confirm the validity of our approach, wedemonstrated this concept by investigating ANE in Fe-based amor-phous materials, commercially known as “Nanomet”41, by tailoringtheir nanostructure. Nanomet is a renowned soft magnetic materialthat contains a high amount of Fe (~ 83-85 at%) and cost-effectivealloying elements (i.e., Cu, B, P, and Si). This material is widelyemployed in high-frequency power electronic devices, such as induc-tors and transformers, owing to its excellent soft magnetic properties.Surprisingly, we found that, although the as-prepared Fe-basedamorphous alloy initially exhibited low ANE, optimal annealing dra-matically increased SANE despite the same average composition, own-ing to the formation of Cu nanoclusters with a large volume fraction.Notably, this material exhibits largest SANE among amorphousalloys34–40. The study involved four steps: (a) starting with the as-quenchedNanomet samples with small ANE, (b) forming Cu clusters inthe amorphous samples, (c) optimizing the density of Cu-rich clustersembedded in an amorphous matrix with a significant enhancement ofANE, and (d) transforming the samples into crystallized Nanomet rib-bons with small ANE with further increasing annealing temperature.These strategies were devised to understand the influence of nanos-tructure on ANE/AEE and provide insights into the thermoelectricproperties of the studiedmaterials. Our work demonstrates that nano-sized Cu-rich clusters in an amorphous matrix of Fe-based soft mag-netic materials (Nanomet) lead to a significant 70% enhancement ofSANE without altering the material chemistry. This strategy resulted inthe figure of merit for ANE comparable to the record-high value in aHeusler ferromagnet at room temperature7. The developed materialsare easily mass-produced at a low cost, and their mechanical flexibilityenables the fabrication of large-area ANE and AEE devices with variousFig. 1 | Anomalous Nernst effect in a nanostructure-engineered magneticmaterial. a–d Schematic illustrations of the anomalous Nernst effect (ANE).∇T, E, andM denote temperature gradient applied to the sample, the electric fielddriven by ANE, and a unit vector of the sample magnetization. It demonstratesnanostructure-engineering of ANE in four different scenarios: (a) Fe-based amor-phous sample (Nanomet), (b) the emergence of nanoprecipitates/clusters in anamorphous matrix, (c) the high-volume density of nanoprecipitates/clustersembedded in an amorphous matrix, indicating high output signals, and (d) thecrystallized Nanomet samples with reduced ANE signals. The same scenario isapplicable to the anomalous Ettingshausen effect (AEE) since ANE is the Onsagerreciprocal of AEE.Article https://doi.org/10.1038/s41467-024-46475-6Nature Communications |         (2024) 15:2184 2shapes. This study and proof of concept thus open new avenues forenhancing the ANE/AEE properties of materials in general through ananostructure engineering approach and discusses the correlationbetween the nanostructure and its transport properties.ResultsNanostructure engineering of amorphous Fe-based ribbonsWe have fabricated 18 ± 2 µm thin and several meters long Nanometribbons using themelt-spinning technique which brings great benefitsfor low manufacturing and raw material costs. Differential scanningcalorimetry analysis of the Nanomet ribbons showed the crystal-lization of α-Fe(Si) and Fe-compound phases at respective onset tem-peratures of Tx1 = 661 K and Tx2 = 806K (Supplementary Fig. 1). Phaseanalysis of the as-quenched (as-spun) sample by X-ray diffraction(XRD) exhibits a broad halo peak indicating the presence of a fullyamorphous phase (Supplementary Fig. 2) whichwas further confirmedby the electron diffraction pattern obtained using transmission elec-tron microscopy (TEM). Figure 2a displays a high-resolution brightfield (BF) scanning (S)TEM image obtained from the as-quenchedsample. The uniform supersaturated solid solutionwith an amorphousstructure was observed in this sample. The amorphous ribbons wereannealed at various isothermal temperatures (573, 623, 643, 653, 673,and 723 K) for only 3min to achieve different microstructural featuresand investigate their correlations with ANE. The microstructure of theannealed samples was studied by high-resolution BF-STEM and elec-tron beam diffraction analysis as shown in Fig. 2b–e. Annealing attemperatures below 653K does not change the amorphous micro-structure, while annealing at temperatures above 673 K leads to thecrystallization of the α-Fe(Si) phase (Supplementary Fig. 2 and Fig. 3).The elements P, B, and C present in the Nanomet alloy composition,are known to be amorphous forming elements42 and this is the mainreason for the formation of an amorphous phase in the as-quenchedribbons, which inhibits the nucleation of α-Fe(Si). Note that theobtained amorphous structure provides excellent flexibility to theribbons developed. As the temperature was increased beyond thecrystallization points, there was a notable reduction in the presence ofamorphous phases, accompanied by an increase in the nucleation ofthe α-Fe(Si) phase. Subsequent annealing at 723 K resulted in a sig-nificant volume fraction of the α-Fe(Si) phase with a larger grain size.Detailed examination through high-resolution TEM images revealedthe distinct separation of the α-Fe(Si) crystals from each other by theresidual amorphous matrix. Moreover, the XRD analysis providedevidence for the appearance of additional diffraction peaks corre-sponding to the crystallization of the Fe-P and Fe-B compounds.Nano-scale elemental analysis of Fe-based ribbonsA question is if there is any nano-scale elemental fluctuation in anamorphous matrix before and/or after crystallization of α-Fe(Si) crys-tals. To answer this question, we conducted atom probe tomography(APT). 3D elemental maps of Fe, P, B, and Cu are shown in Fig. 3a–d.The illustratedmaps are ~10 nm thin sliced fromwholedata for a bettervisualization of the elemental distributions. A uniform distribution ofall elements was observed in the as-quenched sample as shown inFig. 3a, indicating its chemically homogeneous solid solution. Asshown in Fig. 3b, a heterogeneity in the distribution of Cu atoms in themicrostructure of the annealed sample at 623 K was detected. Thisobservation strongly implies the occurrence of Cu clustering, indi-cated by the segregation of Cu atoms. As the annealing temperaturewas raised to 653K, Cu clustering became more visible as demon-strated in Fig. 3c, with an increase in both the size and number densityof nano-sized Cu-rich clusters (Supplementary Fig. 4). The average sizeof the Cu clusters for the Nanomet sample annealed at 653K wasdetermined to be approximately 2.2 nm, with an estimated numberdensity of 7.3 × 1023m−3. Notably, no crystallization was observed up to653 K (Fig. 2d), indicating the presence of Cu clusters dispersed withinthe amorphous matrix. However, due to the absence of discerniblefringe contrast in the nanobeam TEM analysis, the specific structure ofthese clusters could not be identified. The clustering phenomenon ofCu in Fe-basedmaterial can be elucidated by considering themarkedlypositive enthalpy ofmixing exhibited by this system. The low solubilitya As-quenched 573 K annealed 623 K annealed653 K annealed 723 K annealedb cd e2 nm 2 nm 2 nm2 nm 200 nm 10 nmFig. 2 | High resolution TEM analysis of annealed Nanomet samples. High-resolution bright field (BF)-STEM images with corresponding nanobeam electrondiffraction patterns obtained from a, as-quenched ribbons and post-annealed attemperatures of 573, 623, 653, and 723 K shown in b–e, respectively. BF-STEMimages of the 723K annealed sample evidence the crystallization of α-Fe(Si) alongwith residual amorphous regions.Article https://doi.org/10.1038/s41467-024-46475-6Nature Communications |         (2024) 15:2184 3of Cu in Fe leads to the formation of Cu-enriched clusters within theamorphous phase, preceding the nucleation of primary α-Fe crystals.These clusters then act as heterogeneous nucleation sites for the pri-mary α-Fe(Si) crystals43. This requires phase separation within theamorphous phase, which can be seen in Fig. 3d where Cu precipitateswere observed in direct contact with α-Fe(Si) grains in a sampleannealed at 723 K. The observed increase in cluster size in conjunctionwith a decrease in number density suggests the occurrence of theclassic Ostwald ripening phenomenon (Supplementary Fig. 4). Thus,the microstructure transformation in the Nanomet melt-spun ribbonoccurs through a series of three distinct stages: (1) an initial amor-phous phase, (2) an amorphous phase with the formation of clusters,and (3) nucleation of an α-Fe(Si) phase at the heterogeneous sites ofclusters trailed by subsequent grain growth, reduction in the amor-phous phase and the appearanceof additional Fe-B compound phases.Thermal transport properties of nanostructure-engineered Fe-based ribbonsThe thermal transport properties of the nanostructure-engineeredNanomet ribbons were investigated. Figure 4a displays the thermalconductivity κ of the annealed samples, estimated via κ = ρdCpD usingthe thermal diffusivity D, specific heat Cp, and material density ρd(Supplementary Figs. 5–8). D was measured using a laser-spot-periodic-heating method based on lock-in thermography (LIT) (see“Methods” section and Supplementary Figs. 5–7)44. No significantchange in the D values was observed for the samples annealed belowthe onset of crystallization temperature (Tx1 = 661 K) and the valueswere found to be in a range of 2.2–2.6 × 10−6 m2s−1. A steep rise inDwasobserved as the crystallization of α-Fe(Si) started in the amorphousmatrix for samples annealed at 673 K and 723K, with an average valueof 3.5 × 10−6 m2s−1 and 4.1 × 10−6 m2s−1, respectively (SupplementaryFig. 6). Cp did not reveal any discernible patterns, with values rangingbetween 0.47 and 0.56 Jg−1K−1 (Supplementary Fig. 8), closely resem-bling the specific heat of pure Fe. Figure 4a shows that κ increases withthe annealing temperature, with a sudden rise in its value after 673K.Thus, the observed variations in κ are primarily attributed to thechanges in D, while Cp remains nearly constant throughout theannealing process. The longitudinal electrical conductivity σ of theannealed samples was also studied to estimate the contribution ofphonons and electrons in κ through the Wiedemann-Franz law45. Fig-ure 4b indicates that σ exhibits a similar trend to κ with a substantialincrease beyond the crystallization temperature. The electron andphonon thermal conductivities were respectively estimated as κe = σLTand κp = κ – κe, with L being the Lorenz number (2.44 × 10−8WΩK−2) andT the absolute temperature (300K; Supplementary Fig. 9). Interest-ingly, phonons and electron have a comparable contribution to thethermal conductivity for the samples annealed below 643K. However,a slight dominance of the phonon contribution was observed for thesample containing a high-density of Cu-clusters (annealed at 653K)and for the samples annealed beyond the crystallization temperature.Hence, κ and σ behaviors can be attributed to the well-ordered atomicstructure in the crystalline materials, which facilitates efficient pho-non/electron transport and thus leads to higher conductivities. Incontrast, the amorphous phase, characterized by structural disorderand more scattering sites, hinders phonon/electron transport, andresulting in the smaller κe and κp values. It is worth noting that in oursamples, the formation of clusters increases κ due to the presence ofCu-rich clusters in the amorphous matrix, while the presence of clus-ters can also affect these properties by introducing additional scat-tering sites for both phonons and electrons. Therefore, the formationof a high-density Cu-clusters in the amorphous matrix facilitates theelectron and phonon transport by reducing the volume fraction of thedisordered structure. In the future, the phonon engineering approachcan be implemented to fine-tune the transport properties46.LargeanomalousNernst effects innanostructure-engineeredFe-based amorphous ribbonsTo investigate the impact ofmicrostructure tailoring on the transversethermoelectric properties, we studied AEE using the thermoelectricimaging technique based on LITmethod. This technique allowed us toexamine the spatial distribution of temperature modulation andsymmetry of AEE. Steady-state AEE signals were analyzed to quantita-tively estimate the anomalous Ettingshausen coefficient (ΠAEE) at roomtemperature (T = 300K) (see Fig. 4c, “Methods” section, and Supple-mentary Fig. 10). The corresponding SANE values of the samples weredetermined through the Onsager reciprocal relation: SANE =ΠAEE/T ≡ΠAEE/300, also presented in Fig. 4c. The magnitude of SANE for theas-quenched samplewas estimated tobe 2.2 µVK−1. This value is alreadyhigher than that for the other polycrystalline Fe-based alloys and anorder of magnitude larger than that for pure Fe2,12. During annealing,the SANE value remained relatively stable up to 623 K. It increased to 2.7µVK−1 for the sample annealed at 643 K and surprisingly shoots up to aFig. 3 | Atomprobe tomographyanalysis of annealedNanomet samples.APTelementalmaps of Fe (blue), P (red), B (green), andCu (orange) indifferent samples: (a) as-quenched, (b) annealed at 623K, (c) annealed at 653K, and (d) annealed at 723K.Article https://doi.org/10.1038/s41467-024-46475-6Nature Communications |         (2024) 15:2184 4remarkably higher value of 3.7 µVK−1 for the sample annealed at 653 K,which is 70% higher than that for the as-quenched sample. However,when the annealing temperature exceeds 673 K and the crystallizationof α-Fe(Si) proceeds, the SANE values decrease. The substantial increasein SANE was only observed for the sample with a high-density of Cu-enriched clusters within the amorphous matrix. This could be attrib-uted to the interfacial spin-orbit interaction at the boundaries betweenthe Fe-based amorphous matrix and the Cu-clusters47. In addition, thecrystallization of α-Fe(Si) leads to a compositional change in theamorphous phase, which could be optimized in the fully amorphoussamples with large ANE. Although the formation of Cu-clusters in theamorphous matrix resulted in the high SANE value, theoretical studiesare desirable to elucidate the microscopic origin28.DiscussionSANE can be described as two components (SI and SII) using the linearresponse equation17: SANE = ρxxαxy � ρAHEαxx � SI + SII. Here, ρxx, ρAHE,αxy, and αxx represent the longitudinal electrical resistivity, anomalousHall resistivity, transverse thermoelectric conductivity, and long-itudinal thermoelectric conductivity, respectively. The intrinsic ANEthat directly converts temperature gradient into a transverse voltage issignified by the component SI, whereas the SII reflects the voltageoriginating from theHall effect of the longitudinal chargeflow inducedby the Seebeck effect (SE) due to the anomalous Hall effect (AHE). TheSII can be rewritten as �SxxρAHEρxx= � Sxxtan θAHE, where Sxx is the Seebeckcoefficient and θAHE is the anomalous Hall angle. To discern the SI andSII contribution to ANE, we estimated the tanθAHE and αxy by con-ducting transverse electric resistivity (ρyx) and Sxx measurements atroom temperature for the Nanomet samples annealed at 643K and653 K. This enables us to gain better understanding on the origin of anincrease in SANE. Table 1 illustrated the estimated values, revealing thatthemagnitude of SII in both samples is considerably smaller comparedto SI. This infers that ANE is primarily governed by the SI componentsdue to the large value of αxy, while the impact of the anomalous Halland Seebeck effects is negligible. The αxy value for the Nanometsamples annealed at 643 K and 653 K was 1.41 and 1.93 Am−1K−1,respectively. This significant difference in αxy values is consistent withthe trend observed in SANE and can be attributed to the presence of ahigh density of nano-size Cu clusters in amorphous matrix.In Fig. 5a, b, we respectively compared the |SANE| and power factor(PF) σS2ANE values for various spin-caloritronic amorphous materialsreported in the literature with the Fe-based amorphous materialsdeveloped in this study. Notably, the Nanomet sample annealed at653 K exhibits a significantly large SANE value (~3.7 µVK−1) and a high PF(~7.7 µWm−1K−2) at room temperature, which is larger than the valuesobserved in all of the conventional spin-caloritronic amorphousmaterials and comparable to the single-crystalline materials reportedso far2,8,10,30. Furthermore, it is important to highlight that most of thebulk polycrystalline materials exhibit |SANE| values of <1 µVK−1, whileonly a few materials possess SANE of >3 µVK−1 at room temperature12,30,such as the SmCo5 (~3.5 µVK−1)32,33 and Co2MnGa (6–8 µVK−1)systems7,8,17,19 (Supplementary Fig. 11). However, both are expensivedue to the existence of Co or Sm and are not flexible. Therefore, it isworth noting that our low-cost and flexible material demonstrates thehigh SANE value at room temperature, achieved through nanostructureengineering. Figure 5c highlights the mechanical flexibility of theNanomet materials below the onset crystallization temperature. Thisfigure vividly demonstrates their remarkable ability to be easily curvedinto various shapes, confirming their suitability for practical applica-tions thatdemandflexibility. This nanostructure engineering approachFig. 4 | Transport properties of annealed Nanomet samples. a–d Annealingtemperature dependence of the thermal conductivity κ (a), electrical conductivityσ (b), anomalous Nernst coefficient SANE and the corresponding anomalousEttingshausen coefficient ΠAEE estimated using the Onsager reciprocal relation at300K (c), and dimensionless figure of merit for ANE ZANE T at 300K (d) for theNanomet samples. The error bars represent the standard deviation of themeasurements.Article https://doi.org/10.1038/s41467-024-46475-6Nature Communications |         (2024) 15:2184 5enables the enhancement of SANE within the samematerials, leading toelevated levels of performance.To assess the effectiveness of the Nanomet ribbons as spin-caloritronic materials for ANE/AEE applications, we estimated thedimensionless figure of merit for ANE through the equation33:ZANET = S2ANEσκ T . As shown in Fig. 4d, the maximum ZANET value wasfound to be 2.2 × 10−4 at T = 300K for the sample annealed at 653 K,which is three orders of magnitude larger than that for pure Fe andcomparable to the record-high SANE values at room temperature forthe SmCo5-type permanent magnets (4.5 × 10−4)32,33 and Co2MnGaHeusler ferromagnet (2.0 × 10−4)7,8,48. This indicates that the Nanometribbons with embedded nano-sized Cu-clusters in an amorphousmatrix can offer an excellent combination of microstructure featuresfor enhancing the transverse thermoelectric conversion properties.From Fig. 4, it can be inferred that the large value of SANE is thedominant factor contributing to the improvement of ZANET. However,it is still insufficient for practical applications. Therefore, SANE andZANET are necessary to be further improved by tailoring the size, dis-tribution, and composition of the clusters and composition of thematrix to achieve the desired functionalities. Larger ZANET can also beaAnnealed at: 623 K 653 K 673 KAs-quenchedi ii iii ivcbFig. 5 | Spin-caloritronic amorphous alloys for the anomalousNernst effect anddemonstration of mechanical flexibility of Nanomet samples. Comparison ofa, the absolute values of SANE and b, power factor for various spin-caloritronicamorphous alloys measured at room temperature. Notably, the Nanomet ribbon(present study) annealed at 653K exhibits the significantly large |SANE| and powerfactor value compared to that for the other reported alloys (Fe-Pt37, FexSn100-x28,CuCr2Se3.9Br0.140, Co100-xGdx36,39, Co67Fe3Cr3Si15Br1238, and Sm20(Co100-xFex)8034).cHighlighting themechanical flexibility of long, thin Nanomet ribbons prepared indifferent conditions: c.i. as-quenched, c.ii. annealed at 623 K, and c.iii. annealed at653K. However, c.iv. reveals the brittleness of the ribbon annealed at 673 K, as itbroke when subjected to bending.Table 1 | The anomalous Hall resistivity ρAHE, tanθAHE, transverse thermoelectric conductivity αxy, Seebeck coefficient Sxx, SI,and SII values at room temperature for the Nanomet samples annealed at 643K and 653KSample ρAHE (× 10−8Ωm) tanθAHE (× 10−2) αxy (Am−1K−1) Sxx (µVK−1) SI (µVK−1) SII (µVK−1)Annealed at 643K 7.80 4.31 1.41 −4.52 2.54 0.20Annealed at 653 K 7.16 4.02 1.93 −6.48 3.44 0.26Article https://doi.org/10.1038/s41467-024-46475-6Nature Communications |         (2024) 15:2184 6obtained by reducing κp through phonon engineering. Furthermore,we validated our nanostructure engineering approach in tailoring ANEusing another Fe-based amorphous material with a higher Cu content(Supplementary Figs. 12–15). Increase of Cu content in the alloy com-position to 1.5 at% led to an increase in the PF to ~8.9 µWm−1K−2 andZANET to ~2.5 × 10−4 (see Supplementary Fig. 15).In conclusion, we propose and demonstrate a novel approach todesign low-cost and flexible spin-caloritronic materials that exhibitlarge ANE through nanostructure engineering. This approach is ofgreat importance for advancing the use of ANE in thermoelectricdevices. These materials have immense potential in the fabrication ofhighly efficient and flexible energy harvesting and thermal manage-ment devices with curvilinear design. This study has established adirect correlation between ANE and engineered nanostructures in aspin-caloritronic material. As a result, we have discovered a newmethodology for tailoring ANE using nanoscale clusters embedded inan amorphous matrix microstructure, which is a proof-of-concept forfuture advancements. The proposed method is applicable to varioussystems via the development of nanocomposite materials, which canopen up a new avenue towards the development of spin-caloritronicmaterials with giant ANE suitable for practical applications.MethodsPreparation of Fe-based amorphous alloyThe master alloy ingot was prepared by melting high-purity elementsof Fe (99.99%), Si (99.99%), Cu (99.9%), B (99.5%), and Fe3P (99%) usingthe vacuum induction melting technique under an Ar atmosphere.Subsequently, the amorphous ribbon was produced using the single-roll melt-spinner. The ingot was melted in a quartz tube and thenejected under an Ar atmosphere at a pressure of 0.02MPa onto arotating copper (Cu) wheel. The tangential speed of the wheel was setat 35m s−1, while the gap between the quartz tube and the rotating Cuwheel was maintained at 0.2mm. The process flow chart was opti-mized to obtain high-quality amorphous ribbons with lengths of sev-eralmeters, awidthof 5mm, and a thickness ranging from 16 to 20μm,as shown in Fig. 5c.For annealing, the samples were placed in quartz tubes and con-nected to a high vacuum turbo pump to avoid oxidation. To achieverapid annealing and to prevent undesired microstructural changesduring heating, the samples were directly inserted into a preheatedtubular furnace. Annealingwasperformed atdifferent temperatures of573, 623, 643, 653, 673, and 723K for a soaking time of 3min. Thetemperature of the ribbons was continuously monitored duringannealing using aK-type thermometer positioned in closeproximity tothe ribbons. Notably, a heating rate of nearly 120 K s−1 was attained,enabling precise temperature control. Further, the ribbons wereallowed to cool naturally to room temperature by removing the quartztube from the furnace.Characterization of samplesThe chemical composition was estimated using inductively coupledplasma optical emission spectrometry (ICP-OES) and was found to beFe84.7Si2.8P3.8B7.8Cu0.7C0.2 (at%). This composition is associated withthe trademark “Nanomet”. The ribbon was cut into rectangular sam-ples with the dimensions of ~ 60 × 5, ~ 10 × 5, and ~ 10 × 1 ± 0.1mm for σand D, and AEE measurements, respectively. The thermal analysis ofthe as-quenched ribbon was carried out by differential scanningcalorimetry (DSC, RigakuTG8120) at a heating rate of 20K/min in anAratmosphere. Thephase analysis of the annealed sampleswas evaluatedby XRD (Rigaku MiniFlex600) with Cr-Kα radiation. Microstructuralstudies were carried out using a transmission electron microscope(TEM, FEI Titan G2 80-200 equipped with a probe corrector). Theelemental distributionwas investigated using atomprobe tomography(APT) in the laser mode, utilizing the CAMECA LEAP 5000 XS instru-ment operating at a repetition rate of 250 kHz. The laser pulse energywas set at 30 pJ, and the experiments were carried out at a base tem-perature of 30 K, maintaining a constant detection rate of 1.5%. Theobtained APT data was subsequently analyzed using CAMECA AP Suit6.1 software. The TEM specimens and APT tipwere prepared by lift-outand annular milling techniques using a dual beam focused ion beam(FEI Helios 5UX).Transport properties measurementThe angular distribution of the in-plane D was measured by means ofthe LIT method. A schematic of the setup is plotted in SupplementaryFig. 5 comprises an infrared camera, a diode laser, a function gen-erator, and a LIT system. The diode laser emits amodulated laser beamdriven by a periodic reference signal at frequency f from the functiongenerator. The modulated beam was focused as a point on the back-side of the opaque sample by an optical setup. The laser heat-point inturn induces in-plane heat waves that diffuse radially within the sam-ple. Simultaneously, the camera images the thermal response on thefront side of the sample. The LIT system processes the thermal imagesaccording to f and outputs the spatial distribution of the lock-inamplitude A and phase ϕ. D can be estimated from the correlationbetween ϕ and the distance r to the periodic point-heat source withinthe circular diffusion area. Hence, the angular distribution of D can beobtained by revolving the analysis around the heating point at angles θ(Supplementary Fig. 5)49.D=πfdϕ=dr� �2 ð1ÞThemeasurementwasperformedwith a science-grade LIT system(ELITE, DCG Systems Inc.) and a diode laser of 638 ±1 nm wavelength(LDM637D.300.500, Omicron Inc.). The laser heat spot is focused to adiameter of ~7 μm at a power P = 10mW and modulated at f = 3Hz. fand P are selected by taking into consideration maximizing the signal-to-noise ratio, reducing the heat loss effect50, and the thermal diffusionlength Λ=ffiffiffiffiffiffiffiffiffiffiffiffiD=πfpdoes not exceed the sample width49. The Cp wasmeasured by differential scanning calorimetry (DSC, Rigaku Thermoplus EV02). The κ at room temperature was estimated asκ =CpρD, ð2Þwhere ρ is the density of the Nanomet ribbons which is around7.46 g cm−3.AEE of all the samples was examined also by means of the LITmethod12. The rectangular Nanomet samples with the dimensions of ~10 × 1 ± 0.1mm2 were used to measure AEE. The sample was fixed on aglass substrate to reduce the heat loss from the sample to the samplestage because of the low thermal conductivity of glass. The two wires(left- and right-side in Supplementary Fig. 10) were connected in seriesand directed the charge current in opposite directions between thewires. The thermal images of the surface of the samples were obtainedby applying a square-wave-modulated periodic charge current withamplitude Jc, frequency f, and zero offset to the ribbons in the x-direction with an applied magnetic field, µ0H along the y-direction(Supplementary Fig. 10). The first harmonic response of the detectedimages was extracted and transformed into A and ϕ images throughFourier analysis. Using this methodology, it is possible to isolate andidentify the sole effect of thermoelectric effects (∝ Jc) without anyinterference from Joule heating (∝ Jc2)32,51,52. In the LIT-based thermo-electric measurements, the A image represents the magnitude ofcurrent-induced temperature modulation and the ϕ image the sign,that is,ϕ ~ 0° (~180°) corresponds to releasing (absorbing) heat, as wellas the time delay of the temperature modulation. The LIT measure-ments were performed by applying Jc = 1.0 A at room temperature(T = 300K), µ0H = ± 1 T, and f = 1.0-10.0Hz. Since the AEE-inducedtemperature modulation shows the H-odd dependence, we calculatedArticle https://doi.org/10.1038/s41467-024-46475-6Nature Communications |         (2024) 15:2184 7the H-odd component of lock-in amplitude Aodd and phase ϕodd byAodd = |A(+H)e–iϕ(+H) – A(–H)e–iϕ(–H) | /2 and ϕodd = –arg[A( +H)e–iϕ(+H)–A(–H)e–iϕ(–H)], where A( +H) [ϕ(+H)] and A(–H) [ϕ(–H)] show the A (ϕ)value measured at µ0H = +1 T and –1 T, respectively. The AEE-inducedtemperature modulation at the steady state Asteadyodd was determined byusing the magnitude of Aodd signals at f = 1.0Hz because of their f-independence in the low f region. The steady-state AEE signals wereanalyzed to quantitatively estimate the ΠAEE values at 300K using theequation33:ΠAEE =πκjΔTAEEj=4jct, ð3Þwhere ΔTAEE represents the temperature change induced by AEEbetween the top and bottom surfaces of the samples, determinedusing |ΔTAEE | = 2Asteadyodd , jc the charge current density, and t the thick-ness of the samples. To estimate the figure of merit, σ was measuredusing a four-probe method.Formeasurements of ρAHE and Sxx, ribbon samples, with awidth of5mm, a length of 10mm, and a thicknessof 12 µm,werefixedona glasssubstrate. To estimate ρAHE, the value of transverse electric resistivityρyx was determined through the Hall measurement using a physicalpropertymeasurement system (PPMS, QuantumDesign, Inc.), where acharge current of 0.1 A was applied along the longitudinal direction(Supplementary Fig. 16). The ρAHE value was determined by extra-polating the slope of the high-field data to zero-field. The Sxx value wasmeasured using the Seebeck Coefficient/Electric Resistance Measure-ment System (ZEM-3, ADVANCE RIKO, Inc.).Reporting SummaryFurther information on research design is available in the NaturePortfolio Reporting Summary linked to this article.Data availabilityThe data that support the findings of this study are available from thecorresponding authors on reasonable request.References1. Goldsmid, H. J. Introduction to Thermoelectricity. (Springer BerlinHeidelberg, 2016).2. Uchida, K., Zhou, W. & Sakuraba, Y. Transverse thermoelectricgeneration using magnetic materials. Appl. Phys. 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R.G. designed the experiments, pre-pared the samples, collected, and analysed the data. R.G., H.S.A. andT.O. conducted atom probe tomography experiments. K.U. conductedAEE measurements and T.H. analysed the AEE data. T.H. performedmeasurements of AHE and Seebeck effect. A.A. and H.N. measured thethermal diffusivity. H.S.A. and K.U. supervised the study. All authorsdiscussed the results and contributed to the preparation and revision ofthe manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-46475-6.Correspondence and requests for materials should be addressed toKen-ichi Uchida or Hossein Sepehri-Amin.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to thepeer reviewof thiswork. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-46475-6Nature Communications |         (2024) 15:2184 9https://doi.org/10.1038/s41467-024-46475-6http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Creation of flexible spin-caloritronic material with giant transverse thermoelectric conversion by nanostructure engineering Results Nanostructure engineering of amorphous Fe-based ribbons Nano-scale elemental analysis of Fe-based ribbons Thermal transport properties of nanostructure-engineered Fe-based ribbons Large anomalous Nernst effects in nanostructure-engineered Fe-based amorphous ribbons Discussion Methods Preparation of Fe-based amorphous�alloy Characterization of samples Transport properties measurement Reporting Summary Data availability References Acknowledgements Author contributions Competing interests Additional information