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[Ken‐ichi Uchida](https://orcid.org/0000-0001-7680-3051), [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), Fuyuki Ando, [Hossein Sepehri‐Amin](https://orcid.org/0000-0002-7856-7897)

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[Hybrid Transverse Magneto‐Thermoelectric Cooling in Artificially Tilted Multilayers](https://mdr.nims.go.jp/datasets/3c7ead50-bf18-4f61-a00d-fdf201eb55aa)

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Hybrid Transverse Magneto‐Thermoelectric Cooling in Artificially Tilted MultilayersRESEARCH ARTICLEwww.advenergymat.deHybrid Transverse Magneto-Thermoelectric Cooling inArtificially Tilted MultilayersKen-ichi Uchida,* Takamasa Hirai, Fuyuki Ando, and Hossein Sepehri-AminIn artificially tilted multilayers comprising two different conductors that arealternately and obliquely stacked, transverse thermoelectric conversionoccurs, in which charge and heat currents are interconverted in theorthogonal direction. Although transverse thermoelectric conversion alsooccurs in homogeneous materials as an intrinsic transport phenomenonowing to the effects of magnetic fields, magnetization, and spins onconduction carriers, such magneto-thermoelectric effects are investigatedindependently of thermoelectrics for artificially tilted multilayers. Here, thisstudy shows that the synergy of these different principles improves theperformance of transverse thermoelectric conversion. Using lock-inthermography techniques, transverse thermoelectric conversion processesare visualized in artificially tilted multilayers and the experiments clarify hownonuniform charge currents are converted into orthogonal heat currents.Through the measurements of temperature change under magnetic fields, thecontributions of the magneto-thermoelectric effects are quantified in theartificially tilted multilayers and magnetically enhanced hybrid transversethermoelectric cooling is demonstrated. By replacing one of the conductors inthe multilayer with permanent magnets, the same functionality is obtainedeven in the absence of magnetic fields, paving the way for the creation of“thermoelectric permanent magnets” that exhibit efficient transversethermoelectric conversion together with spontaneous magnetization. Thisstudy provides a new material design guideline for transverse thermoelectrics.1. IntroductionThermoelectric cooling is a promising technology for the effi-cient thermal management of electronic devices.[1] Conventionalthermoelectric cooling is driven by the Peltier effect, in which acharge current Jc applied to a conductor is converted into a heatcurrent Jq. Because of the parallel relationship between Jc and Jq,K. Uchida, T. Hirai, F. Ando, H. Sepehri-AminNational Institute for Materials ScienceTsukuba 305-0047, JapanE-mail: uchida.kenichi@nims.go.jpThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/aenm.202302375© 2023 The Authors. Advanced Energy Materials published byWiley-VCH GmbH. This is an open access article under the terms of theCreative Commons Attribution License, which permits use, distributionand reproduction in any medium, provided the original work is properlycited.DOI: 10.1002/aenm.202302375the Peltier effect is classified as a lon-gitudinal thermoelectric effect. Due tothe longitudinal geometry, a thermoelec-tric module based on the Peltier effectusually consists of many pairs of p- andn-type conductors arranged alternatelyand connected in series. Such a com-plex 3D structure consisting of manyjunctions often has problems such aslow mechanical durability, high man-ufacturing costs, and efficiency lossesdue to contact resistances.[2] These is-sues limit the applicability of thermo-electric cooling technologies. The sameproblems apply to thermoelectric powergeneration based on the Seebeck effect.Research on transverse thermoelec-tric effects is gaining momentum withthe aim of improving the versatilityof thermoelectric conversion technolo-gies and expanding their applications.[3]Transverse thermoelectric effects allowthe interconversion between Jc and Jqin the orthogonal direction. Owing tothis feature, simple and versatile ther-moelectric cooling as well as powergeneration can be achieved. The out-put power of transverse thermoelec-tric conversion can be increased by in-creasing the size of materials withoutconstructing complex 3D structures, and the energy losses dueto intermediated electrodes and substrates can be reduced. Al-though transverse thermoelectric conversion has many advan-tages, it is still in the basic research phase owing to vari-ous issues; e.g., its thermopower has not reached a practicallevel.Transverse thermoelectric conversion is driven by six prin-ciples that can be broadly classified into phenomena occur-ring in homogeneous materials and those occurring in hy-brid/composite materials.[3] The former phenomena includethe ordinary and anomalous Nernst/Ettingshausen effects[4–12]and goniopolarity,[13] while the latter includes the spin See-beck/Peltier effect[14–16] and Seebeck/Peltier-driven transversethermoelectric conversion in magnetic/thermoelectric hybridmaterials[17] and in artificially tilted multilayers.[18–27] As typi-fied by the Nernst/Ettingshausen effects, most transverse ther-moelectric effects appear in conductors under external mag-netic fields or in magnetic materials with spontaneous mag-netization, and these effects have been actively investigated inAdv. Energy Mater. 2024, 14, 2302375 2302375 (1 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbHhttp://www.advenergymat.demailto:uchida.kenichi@nims.go.jphttps://doi.org/10.1002/aenm.202302375http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Faenm.202302375&domain=pdf&date_stamp=2023-11-29www.advancedsciencenews.com www.advenergymat.deFigure 1. LIT measurements of thermoelectric effects in an artificially tilted multilayer. a) Schematic of the measurement setup for LIT. Jc denotes a chargecurrent applied to a sample. By using an electromagnet, a magnetic field H with magnitude H was applied to a sample in the transverse direction, i.e.,y direction. b) Schematic of the artificially tilted multilayer sample. The blue and orange parts of the sample correspond to Bi88Sb12 and Bi0.2Sb1.8Te3,respectively, for the samples used for Figures 2–7. Jq and 𝜃 denote the net direction of a heat current generated by the transverse thermoelectric effectsand tilt angle in the artificially tilted multilayer. c) Input charge current and output temperature changes induced by the thermoelectric effects and Jouleheating during the LIT measurements. f and Jc represent the frequency and amplitude of the square-wave-modulated alternating charge current appliedto the sample, respectively. In all the LIT measurements, we fixed Jc = 1 A. d) Example of the lock-in amplitude A and phase 𝜙 images for the artificiallytilted Bi88Sb12/Bi0.2Sb1.8Te3 multilayer.the fields of spin caloritronics[28–30] and topological materialsscience.[9,12] In contrast, transverse thermoelectric conversionin goniopolar materials and artificially tilted multilayers doesnot require magnetic fields or magnetization and appear dueto anisotropic carrier conduction originating from anisotropiccrystalline and artificial structures, respectively, i.e., the off-diagonal Seebeck/Peltier effect. Despite having similar function-alities, these transverse thermoelectric conversion phenomenahave been studied independently. Their interdisciplinary fusionwill bring innovation to transverse thermoelectrics, potentiallysolving the technological problems associated with thermoelec-tric converters.In this study, we demonstrate hybrid transverse thermoelec-tric cooling by superimposing magneto-thermoelectric effectson artificially tilted multilayers. Using thermoelectric imag-ing techniques based on lock-in thermography (LIT),[16,31,32]we experimentally visualize the transverse thermoelectric cool-ing processes due to the structure-induced off-diagonal Peltiereffect (ODPE) in artificially tilted multilayers. When themultilayers exhibit the magneto-Peltier effect (MPE)[33] andordinary Ettingshausen effect (OEE),[4–7] LIT-based thermo-electric imaging under magnetic fields allows us to sepa-rate the temperature change signals due to structure-inducedODPE from those due to MPE and OEE and to estimateeach contribution quantitatively. An appropriate design ofthe multilayer structure and magnetic-field direction H con-sidering the symmetry of the magneto-thermoelectric effectsmakes it possible to improve the performance of trans-verse thermoelectric cooling through the hybridization ofmultiple phenomena. This result provides a novel guide-line for increasing the thermopower and figure of meritof transverse thermoelectric conversion, leading to the de-velopment of versatile and efficient thermal managementtechnologies.2. Results and Discussion2.1. Thermoelectric Conversion Mechanism and Sample SystemThe artificially tilted multilayer for transverse thermoelec-tric conversion consists of two different conductors that arestacked obliquely and alternately (Figure 1b). In this structure,anisotropic conduction of electrons and holes results in the finiteoff-diagonal terms of the thermoelectric transport tensor, makingthe multilayer into a transverse thermoelectric converter.[18–27]In other words, transverse thermoelectric conversion in the arti-ficially tilted multilayer originates from the anisotropic structureitself, and is driven by the longitudinal Seebeck/Peltier effect.This process occurs to the maximum degree when one of theconstituent materials is a p-type thermoelectric material andthe other is an n-type material but occurs even with the samecarrier type when the magnitude of the Seebeck/Peltier coef-ficient is different from each other. Transverse thermoelectricgeneration using such multilayers has been studied for manyyears, and the transverse thermopower and figure of merit canbe designed by selecting appropriate constituent materials andoptimizing the tilt angle and device geometry.[18–27] Transversethermoelectric conversion has been demonstrated in not onlymacroscale bulk materials but also nanoscale superlattices withtilted structures, which are often referred to as (p × n)-typemultilayers,[34,35] although we focus only on bulk stacks in thisstudy. However, the contributions of the magneto-thermoelectriceffects in artificially tilted multilayers have not beeninvestigated.How do the magneto-thermoelectric effects contribute totransverse thermoelectric conversion in artificially tilted multi-layers? In the following, we focus our discussion on charge-current-induced temperature modulation processes, with an em-phasis on their deployment in thermoelectric cooling. First,Adv. Energy Mater. 2024, 14, 2302375 2302375 (2 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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.advenergymat.dewww.advancedsciencenews.com www.advenergymat.deTable 1. Transport coefficients of Bi88Sb12, Bi0.2Sb1.8Te3, and Nd2Fe14B-type magnet used in this study. 𝜎, 𝜅, SS(N), and ZS(N)T represent the electricalconductivity, thermal conductivity, Seebeck (Nernst) coefficient, and dimensionless figure of merit for the Seebeck (Nernst) effect with T being theabsolute temperature, respectively.Material Bi88Sb12 Bi0.2Sb1.8Te3 Nd2Fe14B-type magnetMagnetic field/state 0 T 0.8 T 0 T 0.8 T Demagnetized Magnetized𝜎 (105 S m−1) 5.88 4.90 1.38 1.38 7.82 7.78𝜅 (W m−1 K−1) 4.7 4.3 1.0 1.0 6.9 7.1SS (10−6 V K−1) −86.7 −108.6 171.0 170.4 −5.9 −6.0SN (10−6 V K−1) n.a. −15.6 n.a. −1.7 n.a. −0.9ZST at 300 K 0.28 0.40 1.23 1.22 1.2 × 10−3 1.2 × 10−3ZNT at 300 K n.a. 8.3 × 10−3 n.a. 1.2 × 10−4 n.a. 2.5 × 10−5recall that MPE refers to the magnetic-field dependence of thePeltier effect and that OEE refers to the generation of Jq in the di-rection of the cross product of Jc and H, both of which appearin conductors under magnetic fields. The transverse thermo-electric conversion performance due to structure-induced ODPEcan increase directly when the Peltier coefficient increases ow-ing to MPE, where it also depends on the electrical and ther-mal magnetoresistances. Furthermore, if the constituent ma-terials of the multilayers exhibit OEE, the Ettingshausen heatcurrent can be superimposed on structure-induced ODPE byproperly selecting the direction of H to follow the symmetryof OEE. The combination of these processes is the simplesthybrid transverse magneto-thermoelectric conversion. Althoughthis study focuses on the magnetic-field-induced effects, simi-lar hybrid transverse thermoelectric conversion via anisotropicMPE[32] and the anomalous Ettingshausen effect[10,32] can beexpected if H is replaced with magnetization using magneticmaterials.In this study, we demonstrate hybrid transverse magneto-thermoelectric cooling based on a combination of structure-induced ODPE, MPE, and OEE. The main samples used are arti-ficially tilted Bi88Sb12/Bi0.2Sb1.8Te3 multilayers, where Bi88Sb12 isan n-type thermoelectric material with large MPE and OEE andBi0.2Sb1.8Te3 is a p-type thermoelectric material with a large figureof merit for the Peltier effect. We confirmed that our Bi88Sb12slabs exhibit a large magnetoresistance, MPE, and OEE com-parable to previous results[36,37] and our Bi0.2Sb1.8Te3 slabs ex-hibit no magnetoresistance and MPE and small OEE (Figures S1,S2, Supporting Information). We prepared two artificially tiltedBi88Sb12/Bi0.2Sb1.8Te3 multilayers with a tilt angle of 𝜃 = 45° anda layer thickness of t = 1.0 mm (Sample A) and with 𝜃 = 21° and t= 0.5 mm (Sample B) by a spark plasma sintering (SPS) method,as described in Section 4. Sample A was designed to optimize themagnetic-field-independent ODPE contribution (Figure S3, Sup-porting Information). To check the dependence of the magneto-thermoelectric effects in the artificially tilted multilayers on 𝜃,Sample B was also prepared, which has a smaller transverse ther-mopower, larger effective electrical conductivity along the chargecurrent, and smaller effective thermal conductivity along the heatcurrent. In Section 2.6, to demonstrate the zero-field operationof the hybrid transverse magneto-thermoelectric conversion, wealso use an artificially tilted multilayer based on permanent mag-nets, in which the Bi0.2Sb1.8Te3 layers are replaced with Nd2Fe14B-type magnets, with 𝜃 = 26° and t= 0.5 mm (Sample C). The trans-port properties of our Bi88Sb12, Bi0.2Sb1.8Te3, and Nd2Fe14B-typemagnet are presented in Table 1.2.2. Visualization of Off-Diagonal Peltier Effect in ArtificiallyTilted MultilayersTransverse thermoelectric conversion processes in artificiallytilted multilayers have been investigated using finite-elementcalculations[22,25] but have not been directly observed experimen-tally. Here, we clarify how nonuniform charge currents in artifi-cially tilted multilayers generate transverse heat currents usingthe LIT technique, which makes it possible to visualize the spa-tial distribution and temporal response of temperature modu-lation induced by thermoelectric effects with high temperatureand spatial resolutions.[16,31,32] In the LIT measurements, whena periodic charge current is applied to a sample, thermal im-ages oscillating at the same frequency as the current are ex-tracted through Fourier analysis (Figure 1a). The thermal imagesobtained are transformed into lock-in amplitude A and phase𝜙 images (Figure 1d). The A image shows the distribution ofthe magnitude of the current-induced temperature modulationand the 𝜙 image shows the distribution of the sign of the tem-perature modulation as well as the time delay due to thermaldiffusion. To observe the thermoelectric effects using the LITmethod, we measured the spatial distribution of infrared radi-ation thermally emitted from the surface of the sample usingan infrared camera while applying a rectangularly-modulated al-ternating charge current with amplitude Jc (= 1 A), frequency f,and zero offset to the sample along the x direction. By extract-ing the first-harmonic response of the detected thermal images,we can separate the contribution of the thermoelectric effects(∝ Jc) from that of Joule heating (∝ Jc2) because Joule heatinggenerated by such an alternating current is constant over time(Figure 1c). By increasing f, we can identify heat-source posi-tions owing to the reduction in the heat diffusion length, andclarify how the Peltier heat generated locally at the junction in-terfaces gives rise to transverse thermoelectric conversion. Thedetected infrared radiation is converted into temperature infor-mation through the calibration described in ref. [32]. During theLIT measurements, an in-plane H (with magnitude H) was ap-plied along the y direction (Figure 1a,b). All the LIT measure-ments were performed at room temperature and atmosphericpressure.Adv. Energy Mater. 2024, 14, 2302375 2302375 (3 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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.advenergymat.dewww.advancedsciencenews.com www.advenergymat.deFigure 2. Transverse thermoelectric conversion at zero magnetic field. a) Schematic of Sample A, i.e., the artificially tilted Bi88Sb12/Bi0.2Sb1.8Te3 mul-tilayer with 𝜃 = 45° and 1.0-mm-thick layers, in the cross-section configuration. b) Steady-state temperature T image for Sample A during the LITmeasurement in the cross-section configuration. c,d) A (c) and 𝜙 (d) images for Sample A for different values of f in the cross-section configuration. e,f)x-directional A and 𝜙 profiles along the white dotted lines in the images in (c,d), respectively. g,h) f dependence of the amplitude Aave and phase 𝜙aveaveraged over one Bi88Sb12/Bi0.2Sb1.8Te3 pair. i–p) Results for the top-side configuration. The data points in (g,h) [(o,p)] were obtained by averaging thetemperature modulation signals in the areas defined by the white rectangles with a size of 183 × 4 (183 × 101) pixels in (c,d) [(k,l)], respectively.Figure 2 shows the results of the LIT measurements forSample A in the absence of a magnetic field. First, we mea-sured the current-induced temperature modulation in a cross-sectional configuration (Figure 2a,b). The LIT images at highlock-in frequencies, for example, f = 10.0 Hz, indicate that theheating/cooling signals are localized near the junction interfacesbetween Bi88Sb12 and Bi0.2Sb1.8Te3. Here, the A signals exhibitmaxima along the oblique interfaces (Figure 2c), whereas the 𝜙values at the positions of the A peaks vary by 180° for the neigh-boring interfaces (Figure 2d). This is indeed the behavior exhib-ited by temperature modulation due to the Peltier effect. Impor-tantly, as shown in the top image in Figure 2c, the magnitudeof the A signals is nonuniform along the oblique junction inter-faces, indicating that the charge current flows nonuniformly inthe artificially tilted multilayers: this is the origin of the transversethermoelectric conversion. These local heat release/absorptionAdv. Energy Mater. 2024, 14, 2302375 2302375 (4 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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.advenergymat.dewww.advancedsciencenews.com www.advenergymat.deFigure 3. Separation of magneto-thermoelectric effects showing even and odd dependences on magnetic fields. a,b) A and 𝜙 images for Sample A atf = 1.0 Hz in the top-side configuration, measured when the magnetic field with 𝜇0H = 0.8 T (a) and −0.8 T (b) was applied along the y direction. 𝜇0denotes the vacuum permeability. c) Aeven and 𝜙even images calculated from the raw images in (a,b). d) Aodd and 𝜙odd images calculated from the rawimages in (a,b). Aeven (Aodd) and 𝜙even (𝜙odd) denote the lock-in amplitude and phase showing the H-even (H-odd) dependence, respectively.sources are broadened by thermal diffusion as f decreases. TheA image at f = 0.1 Hz, which reflects a nearly steady-state tem-perature distribution, shows triangle-patterned signals with anangle corresponding to 𝜃 = 45°, and the 𝜙 values vary from ≈0°(red regions) to ≈180° (blue regions) along the y direction (see thebottom images in Figure 2c,d). As indicated by the line profilesin Figure 2f, the 𝜙 values along the white dotted line in Figure 2dare almost uniformly 180° at f = 0.1 Hz, indicating that the en-tire surface is cooled by the longitudinal charge current in thesteady state. This behavior is evident in the results for the top-side configuration (Figure 2i–n); the almost uniform 𝜙 values inthe bottom image in Figure 2l confirm that the alternately tiltedmultilayer functions as the transverse thermoelectric converter,although the A values change periodically along the x directionowing to the junction structures.Figure 2g,h (2o,p) shows the f dependence of the A and 𝜙 val-ues averaged over one Bi88Sb12/Bi0.2Sb1.8Te3 pair, which are de-noted as Aave and 𝜙ave, respectively, in the cross-section (top-side)configuration, where the averaged area is marked with a whiterectangle in Figure 2c (2k) (note that the rectangle in Figure 2cappears as a white line to extract the information near the sam-ple edge). The magnitude of Aave increases monotonically witha reduction in f, approaching the steady-state temperature mod-ulation magnitude. The signal magnitude at low f values in thetop-side configuration exceeds that in the cross-section config-uration, even though the results are for the same sample. Thissuggests that it is difficult to obtain the magnitude of the temper-ature modulation at the topmost surface in the cross-section con-figuration due to the limitation of the spatial resolution (≈20 μm)of the thermal images and slightly rounded sample corners, andthat the top-side configuration is suitable for quantitative dis-cussions about the transverse thermoelectric conversion perfor-mance. Therefore, in the following, only the results for the top-side configuration are presented.2.3. Magneto-Thermoelectric Effects in Artificially TiltedMultilayersNow we are in a position to discuss the contributions of themagneto-thermoelectric effects in the artificially tilted multilay-ers. The temperature change due to MPE (OEE) is known toexhibit an even (odd) dependence on H. Thus, to quantify theMPE and OEE contributions, we acquired LIT images underpositive and negative magnetic fields and separated the H-even-dependent component from the H-odd-dependent componentusing the following equations:Aeven = |||A (+H) e−i𝜙(+H) + A (−H) e−i𝜙(−H)||| ∕2 (1)𝜙even = − arg[A (+H) e−i𝜙(+H) + A (−H) e−i𝜙(−H)] (2)Aodd = |||A (+H) e−i𝜙(+H) − A (−H) e−i𝜙(−H)||| ∕2 (3)𝜙odd = − arg[A (+H) e−i𝜙(+H) − A (−H) e−i𝜙(−H)] (4)Here, Aeven (Aodd) and 𝜙even (𝜙odd) respectively represent thelock-in amplitude and phase exhibiting the H-even (H-odd) de-pendence, which includes the MPE (OEE) contribution (notethat the H-independent contribution is included in Aevenand 𝜙even).[32,37]Figure 3a,b shows the raw A and 𝜙 images for Sample A in thetop-side configuration at f = 1.0 Hz and 𝜇0H = 0.8 T (a, H || +ydirection) and −0.8 T (b, H || −y direction). By substituting thedata in the raw images into Equations (1)–(4), we obtained theAeven (Aodd) and 𝜙even (𝜙odd) images at 𝜇0|H| = 0.8 T, as shown inFigure 3c (3d). The H-even- and H-odd-dependent componentsexhibit different temperature distributions, suggesting that thetemperature changes are caused by several different thermoelec-tric effects.Figure 4c shows the |H| dependence of the Aeven signal forSample A around the Bi88Sb12/Bi0.2Sb1.8Te3 interface position,marked with a white rectangle in Figure 4a, at f = 1.0 Hz.With an increase in |H|, the Aeven signal increases monotonically,while the 𝜙even values remain constant (Figure 4b,d). This non-saturating magnetic-field dependence is consistent with the be-havior of the magneto-Seebeck effect, i.e., the reciprocal of MPE,in Bi88Sb12 (Figure S1a,b in the Supporting Information). Thus,we conclude that the field-induced enhancement of the Aeven sig-nals in the artificially tilted Bi88Sb12/Bi0.2Sb1.8Te3 multilayer isdue to MPE in Bi88Sb12.Adv. Energy Mater. 2024, 14, 2302375 2302375 (5 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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.advenergymat.dewww.advancedsciencenews.com www.advenergymat.deFigure 4. Contribution of MPE. a,b) Aeven (a) and 𝜙even (b) images forSample A at f = 1.0 Hz and 𝜇0|H| = 0.8 T in the top-side configuration.c,d) |H| dependence of the Aeven (c) and 𝜙even (d) signals at f = 1.0 Hz.The data points in (c) and (d) were obtained by averaging the temperaturemodulation signals in the area defined by the white rectangles with a sizeof 6 × 101 pixels in (a,b), respectively.Figure 5a,b shows the Aodd and 𝜙odd images for Sample A at𝜇0|H| = 0.8 T for different values of f. Clear Aodd signals appearonly in the Bi88Sb12 regions and their magnitudes increase witha reduction in f (Figure 5c). As shown in Figure 3c,d, the posi-tions of the Aodd signals deviated from those of the Aeven signals.The almost uniform 𝜙odd values of ≈180° at low f indicate thatthe transverse thermoelectric cooling also occurs in the H-odd-dependent component (see the bottom image in Figure 5b andthe f dependence of 𝜙odd in Figure 5d). The |H| dependence ofthe Aodd signal for Sample A in the Bi88Sb12 region, marked witha white rectangle in Figure 5a, at f = 1.0 Hz is plotted as blue cir-cles in Figure 5e. The Aodd signal increases with increasing |H|and becomes saturated for 𝜇0|H| >0.6 T, while the 𝜙odd valuesremain constant (Figure 5e,f). This behavior is consistent withthe magnetic-field dependence of the transverse thermopowerdue to the ordinary Nernst effect, i.e., the reciprocal of OEE, inBi88Sb12 (see the black curve in Figure 5e; Figure S2, Support-ing Information). This result confirms that OEE also gives rise tothe transverse thermoelectric conversion in the artificially tiltedBi88Sb12/Bi0.2Sb1.8Te3 multilayer.Because the total output is important for actual thermoelectricapplications, we next estimated the H dependence on the temper-ature modulation signal averaged over one Bi88Sb12/Bi0.2Sb1.8Te3pair, i.e., Aave, which includes structure-induced ODPE, MPE,and OEE. Figure 6a shows the Aave signal as a function of H forSample A at f = 0.1 Hz. The magnitude of Aave exhibits a clear Hdependence and is increased by applying a positive field owingto the superposition of MPE and OEE. As indicated by the closedcircles in Figure 6b, the H-induced enhancement ratio for Sam-ple A is estimated to be 𝛿 ≡ [Aave(H) − Aave(0 T)]/Aave(0 T) ≈11%for 𝜇0H >0.6 T. The 𝛿 value can be further increased by optimiz-ing 𝜃 and t for the artificially tilted multilayers. To demonstratethis, we performed the same measurements on Sample B withdifferent 𝜃 and t values. The open-circle data points in Figure 6bindicate that 𝛿 reaches ≈15% for Sample B at 𝜇0H = 1.0 T (seealso the raw LIT data for Sample B in Figure S4, SupportingInformation).Figure 5. Contribution of OEE. a,b) Aodd (a) and 𝜙odd (b) images for Sample A at 𝜇0|H| = 0.8 T for different values of f in the top-side configuration. c,d)f dependence of the Aodd (c) and 𝜙odd (d) signals at 𝜇0|H| = 0.8 T. e,f) |H| dependence of the Aodd (e) and 𝜙odd (f) signals at f = 1.0 Hz (blue circles). Theblack curve in (e) shows the |H| dependence of the magnitude of the transverse thermoelectric voltage |V| for a Bi88Sb12 slab at a temperature differenceof ΔT = 4.2 K (see also Figure S2, Supporting Information). The data points in (c–f) were obtained by averaging the temperature modulation signals inthe areas defined by the white rectangles with a size of 69 × 101 pixels in (a,b).Adv. Energy Mater. 2024, 14, 2302375 2302375 (6 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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.advenergymat.dewww.advancedsciencenews.com www.advenergymat.deFigure 6. Magnetic-field dependence of averaged temperature modula-tion. a) H dependence of the Aave signal for Sample A at f = 0.1 Hz.b) H dependence of 𝛿 ≡ [Aave(H) − Aave(0 T)]/Aave(0 T) for Sample A(closed circles) and Sample B (open circles), i.e., the artificially tiltedBi88Sb12/Bi0.2Sb1.8Te3 multilayer with 𝜃 = 21° and 0.5-mm-thick layers,at f = 0.1 Hz. The data points in this figure were obtained by averaging thetemperature modulation signals in the area defined by the white rectanglein Figure 2k.2.4. Steady-State Hybrid Transverse Magneto-ThermoelectricCoolingThe experiments presented in Section 2.3 revealed that both MPEand OEE enhance the transverse thermoelectric conversion inartificially tilted multilayers. Here, we demonstrate that the hy-brid transverse magneto-thermoelectric conversion is useful forsteady-state cooling. Although the contribution of Joule heatingwas excluded in the LIT measurements, the competition betweenthe thermoelectric effects and Joule heating must be consideredunder steady-state conditions. We measured the current-inducedtemperature change ΔTave from room temperature averaged overthe Bi88Sb12/Bi0.2Sb1.8Te3 junction with a constant charge currentI applied along the x direction. To obtain steady-state ΔTave val-ues, the temperature of the sample surface was recorded afterwaiting 30 s from the I application using standard thermographyinstead of LIT. Figure 7a shows the ΔTave values as a function ofFigure 7. Steady-state hybrid transverse magneto-thermoelectric cooling.a) Charge-current I dependence ofΔTave, i.e., the steady-state temperaturechange from room temperature averaged over one Bi88Sb12/Bi0.2Sb1.8Te3pair, at 𝜇0H = 0.8 T (diamonds) and −0.8 T (triangles). b) |I| dependenceof ΔTTE, i.e., the steady-state temperature change from room temperatureinduced by the thermoelectric effects. c) |I| dependence of ΔTJ, i.e., thesteady-state temperature change from room temperature induced by Jouleheating.I for Sample B at 𝜇0H = 0.8 and −0.8 T. The shifted parabolicΔTave–I curves indicate that ΔTave is determined by the compe-tition between the thermoelectric effects (∝ I) and Joule heating(∝ I2). The region ΔTave <0 K for I >0 A corresponds to steady-state cooling, in which the contribution of thermoelectric coolingexceeds that of Joule heating. Importantly, the ΔTave–I curves ex-hibit a significant shift depending on H; the steady-state coolingperformance is improved by applying a positive field, where themaximum value of ΔTave = −6 K occurs at I = 5 A. The contri-butions of the thermoelectric effects and Joule heating can be es-timated from ΔTTE = [ΔT(+I) − ΔT(−I)]/2 and ΔTJ = [ΔT(+I)+ ΔT(−I)]/2, respectively, where ΔT(+I) [ΔT(−I)] denotes theΔTave value at a positive (negative) current. As expected, the ΔTTEsignal is proportional to I, whereas the ΔTJ signal is proportionalto I2 (Figure 7b,c). The magnitude of ΔTTE is enhanced by ap-plying positive H owing to the contributions of the magneto-thermoelectric effects, but ΔTJ is independent of the sign of Hbecause the magnetoresistance exhibits the H-even dependence(Figure S1c,d in the Supporting Information). As the relativeAdv. Energy Mater. 2024, 14, 2302375 2302375 (7 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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.advenergymat.dewww.advancedsciencenews.com www.advenergymat.deFigure 8. Transverse thermoelectric conversion in an artificially tilted multilayer based on permanent magnets. a) Schematic of Sample C, i.e., the artifi-cially tilted Bi88Sb12/Nd2Fe14B multilayer with 𝜃 = 26° and 0.5-mm-thick layers, in the top-side configuration. M denotes the spontaneous magnetizationof the Nd2Fe14B-type magnets. b) Photograph of the artificially tilted Bi88Sb12/Nd2Fe14B multilayer block with magnetic metal spheres attached by at-traction due to the remanent magnetization of the Nd2Fe14B-type magnets. c,d) A and 𝜙 images for Sample C with the magnetized Nd2Fe14B-typemagnet layers at f = 10.0 and 0.5 Hz in the cross-section (c) and top-side (d) configurations. e) H dependence of the magnetization M of the Nd2Fe14B-type magnet at room temperature. f) f dependence of the Aave signal for Sample C with the magnetized (red circles) and demagnetized (black circles)Nd2Fe14B-type magnet layers in the top-side configuration. The inset of (f) shows the f dependence of 𝛿M = (Aave,mag − Aave,demag)/Aave,demag, whereAave,mag (Aave,demag) denotes Aave in the magnetized (demagnetized) state. The data points in (f) were obtained by averaging the temperature modula-tion signals in the area defined by the white rectangle with a size of 150 × 101 pixels in (d). All the LIT data in this figure were measured in the absenceof an external magnetic field.contributions of the thermoelectric effects and Joule heating de-pend on the thermal boundary conditions, the steady-state cool-ing performance can be improved by optimizing the thermal de-sign of the device.2.5. Estimation of Figure of MeritIn this section, we estimate the magnetic-field dependence of thefigure of merit for the artificially tilted Bi88Sb12/Bi0.2Sb1.8Te3 mul-tilayer. The figure of merit ZTT for transverse thermoelectric con-version is defined as:ZTT =S2T𝜎xx𝜅zzT (5)where ST, 𝜎xx, and 𝜅zz represent the total transverse ther-mopower, effective electrical conductivity along the charge cur-rent (x-direction), and effective thermal conductivity along theheat current (z-direction), respectively. The transverse ther-mopower due to structure-induced ODPE, 𝜎xx, and 𝜅zz can becalculated analytically using equations in the literature.[18–27] Thecontributions of MPE and the electrical and thermal magnetore-sistances can be introduced as the field dependence of the trans-port coefficients in the equations for determining the ODPE-driven transverse thermopower, 𝜎xx, and 𝜅zz. However, in ourartificially tilted multilayers, ST includes not only the structure-induced ODPE and MPE contributions but also the OEE contri-bution. Analytical calculation of the OEE contribution is difficultbecause of the nonuniform flows of charge and heat currents.Therefore, we measured the transverse thermoelectric voltage inSamples A and B by applying a temperature gradient and mag-netic field and experimentally estimated the ST values (Figure S5,Supporting Information). By combining the measured ST valueswith the calculated 𝜎xx and 𝜅zz values, we determined the figuresof merit for Sample A (Sample B) at 300 K to be ZTT = 0.20, 0.17,and 0.14 (0.15, 0.13, and 0.10) at 𝜇0H = 0.8, 0, and −0.8 T, re-spectively. These results confirm that ZTT in the artificially tiltedmultilayers can be enhanced by the magneto-thermoelectriceffects.2.6. Hybrid Transverse Magneto-Thermoelectric Conversion inArtificially Tilted Multilayer Based on Permanent MagnetsDespite the usefulness of the magneto-thermoelectric effects, theapplication of an external magnetic field often hinders thermo-electric applications. To overcome this problem, we demonstratehybrid transverse magneto-thermoelectric conversion in the ab-sence of an external magnetic field by incorporating permanentmagnets into an artificially tilted multilayer. Figure 8a shows aschematic of the artificially tilted Bi88Sb12/Nd2Fe14B multilayerwith anisotropic Nd2Fe14B-type magnets that can be magnetizedonly in the direction perpendicular to the stacking plane. Whenthe Nd2Fe14B layers are magnetized, stray fields due to the re-manent magnetization of the Nd2Fe14B layers are applied to theBi88Sb12 layers, which drive the magneto-thermoelectric effectsAdv. Energy Mater. 2024, 14, 2302375 2302375 (8 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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.advenergymat.dewww.advancedsciencenews.com www.advenergymat.dein Bi88Sb12. The photograph in Figure 8b shows that the block ofthe artificially tilted Bi88Sb12/Nd2Fe14B multilayer functions as apermanent magnet; the Nd2Fe14B layers exhibit a strong coerciveforce and remanent magnetization even after bonding them withthe Bi88Sb12 layers (Figure 8e). Sample C was cut from this largeblock.Figure 8c (8d) shows the A and 𝜙 images for Sample C at f= 10.0 and 0.5 Hz in the cross-section (top-side) configuration.Although the temperature distributions for Sample C are qual-itatively similar to those for Samples A and B, the sign of thetransverse thermoelectric conversion for Sample C is oppositeto that for Samples A and B because the Seebeck/Peltier coef-ficient of the Nd2Fe14B-type magnet is opposite in sign to thatof Bi0.2Sb1.8Te3 (Table 1). Figure 8f presents a comparison of thef dependence of the Aave signals at 𝜇0H = 0 T for Sample Cmeasured before and after magnetizing the Nd2Fe14B layers. Themagnitude of the temperature change is significantly increasedby magnetizing the Nd2Fe14B layers over the entire f range, con-firming the contribution of the magneto-thermoelectric effects.As shown in the inset of Figure 8f, the magnetization-dependentenhancement ratio for Sample C is estimated to be 𝛿M = (Aave,mag− Aave,demag)/Aave,demag ≈ 8% in the absence of an external field,where Aave,mag (Aave,demag) denotes the Aave value in the magne-tized (demagnetized) state. Because of the small Seebeck/Peltiercoefficient of the Nd2Fe14B-type magnet, the magnitude of theAave signals for Sample C is one order of magnitude smaller thanthat for Samples A and B. Nevertheless, this experiment clearlyindicates that the hybrid transverse magneto-thermoelectric con-version can be achieved without an external magnetic field, sug-gesting the importance of developing permanent magnets withlarge Seebeck/Peltier coefficients to realize efficient transversethermoelectric conversion. The transverse thermoelectric con-version performance in the artificially tilted multilayers basedon permanent magnets may also be improved by stacking threedifferent materials, i.e., a permanent magnet and p- and n-typeconductors showing large Seebeck/Peltier coefficients as well aslarge magneto-thermoelectric effects.Finally, we discuss the origin of the magnetization-dependentenhancement of the transverse thermoelectric conversion in theartificially tilted multilayer based on permanent magnets. Al-though the remanent magnetization of the Nd2Fe14B layers gen-erates a magnetic field in the Bi88Sb12 layers, the configura-tion in Figure 8a does not satisfy the symmetry of OEE be-cause of the absence of the magnetization component in thedirection of the cross product of Jc and Jq. Thus, in Sam-ple C, MPE is expected to manifest directly. However, be-cause the stray field is non-uniform near the surfaces of thesample, a finite OEE contribution may also appear. To opti-mize artificially tilted multilayers based on permanent mag-nets, the design of not only transverse thermoelectric prop-erties but also stray-field distributions is required. The useof isotropic magnets facilitates the control of the stray-fielddistributions.3. ConclusionWe demonstrated the hybrid transverse thermoelectric coolingby multiple phenomena including the magneto-thermoelectriceffects in artificially tilted multilayers. Using the thermoelectricimaging technique based on LIT, the transverse thermoelectriccooling processes in the artificially tilted Bi88Sb12/Bi0.2Sb1.8Te3multilayers were clarified. The LIT measurements under mag-netic fields allowed us to separate the contributions of themagneto-thermoelectric effects exhibiting the even dependenceon the magnetic field, i.e., MPE, and odd dependence, i.e., OEE,from the field-independent ODPE contribution. Through the sys-tematic measurements and analyses, we quantified the contri-butions of each magneto-thermoelectric effect, and found thatboth MPE and OEE can improve the steady-state cooling ca-pability and figure of merit of the artificially tilted multilay-ers. Furthermore, by replacing one of the constituent mate-rials in the multilayer with permanent magnets, we demon-strated that hybrid transverse magneto-thermoelectric conver-sion can operate even in the absence of a magnetic field. Theartificially tilted multilayers based on permanent magnets func-tion as “thermoelectric permanent magnets” that have hightransverse thermoelectric conversion performance together withspontaneous magnetization. This concept provides an un-conventional strategy for increasing the transverse magneto-thermoelectric conversion efficiency and suggests the possi-bility of transforming omnipresent permanent magnets intofunctional materials that enable electronic cooling and ther-mopower generation. Practical applications of the hybrid trans-verse magneto-thermoelectric conversion require the develop-ment of stable n- and p-type materials that exhibit large magneto-thermoelectric effects, simultaneous achievement of the largemagneto-thermoelectric conversion and its zero-field operation,reduction of the thermal conductivity by nanostructuring orphonon engineering,[38,39] and development of module struc-tures suitable for this operation principle.4. Experimental SectionSample Preparation and Characterization: Samples A and B, i.e., the ar-tificially tilted Bi88Sb12/Bi0.2Sb1.8Te3 multilayers, were prepared as follows.First, homogenous Bi88Sb12 and Bi0.2Sb1.8Te3 alloy slabs were synthe-sized. BiSb alloy powder (99.99% purity), obtained from Kojundo Chem-ical Laboratory Co., Ltd., was crushed using a planetary ball mill (PL-7, Fritsch Japan Co., Ltd.) at 350 rpm for 30 min. The crushed powderwas then sieved through a 63-μm mesh. Next, a cylindrical Bi88Sb12 in-got with a diameter of 10 mm was prepared via the SPS method under apressure of 50 MPa at 245 °C for 5 min in vacuum conditions. A cylin-drical Bi0.2Sb1.8Te3 ingot with a diameter of 10 mm was also preparedvia the SPS method under a pressure of 30 MPa at 445 °C for 4 min invacuum conditions by using BiSbTe alloy powder (99.9% purity) with aparticle size of <74 μm, which was obtained from Toshima Manufactur-ing Co., Ltd. The Bi88Sb12 and Bi0.2Sb1.8Te3 alloys are polycrystalline andtheir grain crystal orientations are random, indicating isotropic transportproperties. Using a diamond wire saw, the ingots were sliced into manydisks with a thickness of 1 mm (0.5 mm) for Sample A (Sample B). TheBi88Sb12 and Bi0.2Sb1.8Te3 discs were alternately stacked and bonded viathe SPS method under a pressure of 30 MPa at 230 °C for 5 h. Finally, thebonded stack was cut into a rectangular shape with a size of ≈10 × 2 × 2mm3 and 𝜃 = 45° (𝜃 = 21°) for Sample A (Sample B) using the dia-mond wire saw. The elemental distributions and compositions of SamplesA and B were characterized by scanning electron microscopy (SEM) andenergy-dispersive X-ray spectroscopy (EDS) using Cross-Beam 1540ESB(Carl Zeiss AG). The samples for the SEM observations were preparedvia mechanical polishing. As shown in Figure S6 (Supporting Informa-tion), the compositions of the bulk regions of Bi88Sb12 and Bi0.2Sb1.8Te3Adv. Energy Mater. 2024, 14, 2302375 2302375 (9 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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.advenergymat.dewww.advancedsciencenews.com www.advenergymat.dewere uniform, although an interdiffusion of ≈30 μm in width was ob-served at the interfaces. Considering the large sample size, it is concludedthat the artificially tilted Bi88Sb12/Bi0.2Sb1.8Te3 multilayers have sharpboundaries.Sample C, i.e., the artificially tilted Bi88Sb12/Nd2Fe14B multilayer, wasprepared as follows. Bi88Sb12 discs with a diameter of 20 mm and thick-ness of 0.5 mm were prepared by the same method used for Samples Aand B. Ni/Cu/Ni-plated anisotropic Nd2Fe14B-type magnet discs were em-ployed with a diameter of 20 mm and thickness of 0.5 mm, which were ob-tained from Magfine Corporation. The Bi88Sb12 and Nd2Fe14B-type mag-net discs were alternately stacked and bonded via the SPS method under apressure of 20 MPa at 245 °C for 1 h. The Nd2Fe14B-type magnets were de-magnetized before the bonding process. The bonded stack was cut into arectangular shape with a size of ≈10 × 2 × 2 mm3 and 𝜃 = 26° using the di-amond wire saw. The elemental distribution in Sample C was characterizedby SEM-EDS. Owing to the presence of the plating layers, the interdiffusionbetween the Bi88Sb12 and Nd2Fe14B-type magnets was negligible (FigureS7, Supporting Information). As boron could not be detected by SEM-EDS,the composition of the Nd2Fe14B-type magnets without plating layers wasmeasured by means of inductively coupled plasma analysis. The compo-sition was determined to be Nd8.3Pr2.7Ce3.4Gd0.7Fe77.2Co0.3B5.9Cu0.2Al1.3(at%), where the oxygen concentration was not analyzed. The anisotropicNd2Fe14B-type magnets can only be magnetized in their magnetic easyaxis, i.e., the direction perpendicular to the stacking plane. To verify that themagnetic properties of the Nd2Fe14B layers were not degraded after sinter-bonding, the Nd2Fe14B-type magnet portion was cut from the multilayer,and its magnetization curve was measured by superconducting quantuminterference device vibrating sample magnetometry using Magnetic Prop-erties Measurement System (MPMS3, Quantum Design Inc.).Thermography Measurements: The LIT measurements were performedusing Enhanced Lock-In Thermal Emission (ELITE, DCG Systems G.K.) atroom temperature and atmospheric pressure. For the LIT measurements,the sample was fixed on a plastic plate with low thermal conductivity toreduce the heat leakage due to thermal conduction. To enhance the in-frared emissivity and ensure uniform emission properties, the top surfaceof the sample was coated with insulating black ink having an emissivityof >0.94 (JSC-3, JAPANSENSOR Corporation). As described above, Sam-ple C was synthesized after demagnetizing the Nd2Fe14B layers. There-fore, the LIT data were first obtained in the demagnetized state. Then, theNd2Fe14B layers were magnetized in the direction perpendicular to thestacking plane by a pulsed magnetic field of 8 T, and the LIT measure-ments were performed for the same sample under the same conditions.During the systematic LIT measurements, all the samples were stable; thethermoelectric response did not change by repeating heating-cooling cy-cles.The steady-state thermography measurements were performed for ob-taining the data in Figure 7 using a different infrared camera (ImageIR8300, InfraTec GmbH). To reduce the Joule heating contribution, SampleB was fixed on an Al block whose surface was anodized because Al has ahigh thermal conductivity. Similar to the LIT measurements, the top sur-face of the sample was coated with black ink.Measurements of Transport Properties: The longitudinal electric con-ductivity of the materials used in this study was measured by the four-probe method. The thermal conductivity was determined through ther-mal diffusivity measured by the laser flash method, specific heat mea-sured by the differential scanning calorimetry, and density measured bythe Archimedes method. The Seebeck coefficient and its magnetic-fielddependence were measured using the method described in ref. [40]. Here,the sample was clamped between two Cu blocks of which the temperatureswere controlled independently with ceramic heaters and temperature sen-sors. For accurate measurements of the Seebeck coefficient, an appliedtemperature difference and generated thermoelectric voltage at the samepositions were measured simultaneously by using two pairs of thermo-couple probes attached to the sample, where the temperature difference(thermoelectric voltage) was estimated from voltage outputs in each ther-mocouple (between the probes). This system is similar to the SeebeckCoefficient/Electric Resistance Measurement System (ZEM-3, ADVANCERIKO, Inc.) but in the system, a magnetic field can be applied in the di-rection perpendicular to the temperature gradient.[40] After stabilizing thetemperatures of the Cu blocks, the Seebeck coefficient of the sample wasestimated by fitting the temperature difference dependence of the thermo-electric voltage with a linear function at room temperature at various val-ues of H. The obtained Seebeck coefficient and figure of merit for the See-beck effect of Bi88Sb12 and Bi0.2Sb1.8Te3 are consistent with the values inthe literature[36,37,41] (note that techniques to increase the figure of merit,e.g., reduction of the thermal conductivity by nanostructuring or phononengineering[38,39] and enhancement of the Seebeck coefficient by energyfiltering through nano-compositing, are not applied to the materials usedin this study). The ordinary Nernst effect of Bi88Sb12 and Bi0.2Sb1.8Te3 wasmeasured using a homemade temperature gradient generator combinedwith an electromagnet via a method similar to that described in ref. [17].A rectangular sample was bridged and fixed on two anodized Al blocks.One of the Al blocks is thermally connected to a heat bath and the otherto a chip heater, where a temperature gradient can be generated by apply-ing a charge current to the heater. The surface of the sample was coatedwith black ink and the magnitude of the applied temperature gradient wasmeasured with the infrared camera. While the magnetic field was sweptin the direction perpendicular to the temperature gradient, the electricvoltage in the direction perpendicular to both the temperature gradientand H was measured. The anomalous Nernst coefficient of the Nd2Fe14B-type magnet, shown in Table 1, was estimated through the LIT measure-ments of the anomalous Ettingshausen effect and the Onsager reciprocalrelation.[10] These measurements were performed at room temperatureand atmospheric pressure using the materials prepared under the sameconditions as those used for Samples A, B, and C.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThe authors thank Y. Oikawa for valuable discussions, and K. Suzuki, M.Isomura, and X. Tang for technical support. This work was supportedby ERATO “Magnetic Thermal Management Materials” (grant no. JPM-JER2201) from JST, Japan.Conflict of InterestThe authors declare no conflict of interest.Author ContributionsK.U. planned and supervised the study, designed the experiments, pre-pared the samples, performed the LIT measurements, developed the ex-planation of the experiments, and prepared the manuscript. K.U., T.H.,and F.A. collected the thermal, thermoelectric, and magnetic propertiesof the samples. T.H. analyzed the LIT data. F.A. analytically calculatedthe transverse thermoelectric conversion properties. H.S.A. performed themicrostructure analyses. All the authors discussed the results and com-mented on the manuscript.Data Availability StatementThe data that support the findings of this study are available from thecorresponding author upon reasonable request.Keywordsartificially tilted multilayers, Ettingshausen effect, lock-in thermography,magneto-Peltier effect, permanent magnets, transverse thermoelectricsAdv. Energy Mater. 2024, 14, 2302375 2302375 (10 of 11) © 2023 The Authors. Advanced Energy Materials published by Wiley-VCH GmbH 16146840, 2024, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aenm.202302375 by Cochrane Japan, Wiley Online Library on [19/01/2024]. 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