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[Yebin Lee](https://orcid.org/0000-0002-0737-1635), [Fuyuki Ando](https://orcid.org/0009-0003-7789-8170), [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), [Rajkumar Modak](https://orcid.org/0000-0001-7939-3289), [Hossein Sepehri‐Amin](https://orcid.org/0000-0002-7856-7897), [Ken‐ichi Uchida](https://orcid.org/0000-0001-7680-3051)

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[Zero‐Field Hybridization of Anomalous Nernst and Off‐diagonal Seebeck Effects in Artificially Tilted Multilayers](https://mdr.nims.go.jp/datasets/2a53ab56-0866-4cbb-91a5-230bcc66d13c)

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Zero‐Field Hybridization of Anomalous Nernst and Off‐diagonal Seebeck Effects in Artificially Tilted MultilayersRESEARCH ARTICLEwww.ann-phys.orgZero-Field Hybridization of Anomalous Nernst andOff-diagonal Seebeck Effects in Artificially Tilted MultilayersYebin Lee, Fuyuki Ando,* Takamasa Hirai, Rajkumar Modak, Hossein Sepehri-Amin,and Ken-ichi Uchida*Hybrid transverse thermoelectric conversion driven by simultaneous action ofmultiple phenomena offers a promising route for efficient energy conversion.This study demonstrates magnetic-field-free hybrid transverse thermoelectricconversion based on the anomalous Nernst and off-diagonal Seebeck effectsin artificially tilted multilayers comprising SmCo5/Bi0.2Sb1.8Te3 junctions,where the remanent magnetization of SmCo5 induces the anomalous Nernsteffect in the absence of an external magnetic field. The thermoelectric figureof merit is observed to be 0.299 ± 0.005 at room temperature owing to theadditive contribution of the anomalous Nernst effect, indicating that theexcellent figure of merit due to the off-diagonal Seebeck effect can further beenhanced by hybridizing the anomalous Nernst effect. These results establisha new approach for high-performance transverse thermoelectric materials,enabling energy harvesting and cooling applications that leveragemagnetically controlled thermoelectric effects without requiring an externalmagnetic field.1. IntroductionThermoelectric materials enable the direct interconversion of aheat current Jq into a charge current Jc and have been extensivelystudied for their potential in energy harvesting and thermalman-agement applications.[1–3] Conventional thermoelectrics is basedon the longitudinal Seebeck and Peltier effects, where Jq and JcY. Lee, F. Ando, T. Hirai, R. Modak, H. Sepehri-Amin, K. UchidaNational Institute for Materials ScienceTsukuba 305-0047, JapanE-mail: ANDO.Fuyuki@nims.go.jp;UCHIDA.Kenichi@nims.go.jpY. Lee, K.UchidaGraduate School of Science andTechnologyUniversity of TsukubaTsukuba 305-8573, JapanR.Modak, K.UchidaDepartment of AdvancedMaterials ScienceGraduate School of Frontier SciencesTheUniversity of TokyoKashiwa 277-8561, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/andp.202500127© 2025 The Author(s). Annalen der Physik published by Wiley-VCHGmbH. This is an open access article under the terms of the CreativeCommons Attribution License, which permits use, distribution andreproduction in any medium, provided the original work is properly cited.DOI: 10.1002/andp.202500127flow in the same direction. To max-imize the thermoelectric output,Seebeck/Peltier-effect-based devicesare usually constructed with alternatelyarranging p- and n-type materials andconnecting them in series. The com-plex structure required for such devicesintroduces challenges, including lowme-chanical durability and energy losses dueto contact resistances at the junctions.[4]Transverse thermoelectric effects, bycontrast, enable the interconversion of Jqand Jc in orthogonal directions, offeringa simplified architecture. By eliminatingsubstrates and junctions, transverse ther-moelectrics can increase thermoelectricconversion efficiency and reduce energylosses, thus addressing the limitations oflongitudinal thermoelectric devices.[5]Transverse thermoelectric conver-sion is driven by various mechanismsincluding the ordinary/anomalous Nernst effect (ONE/ANE)[6–13]induced by a magnetic field/spontaneous magnetization and theoff-diagonal Seebeck/Peltier effect (ODSE/ODPE). ODSE andANE are the thermoelectric generation effects that induce Jcperpendicular to the applied temperature gradient. In contrast,ODPE and the anomalous Ettingshausen effect (AEE) are the On-sager reciprocals of ODSE and ANE, respectively, that induce Jqperpendicular to the applied charge current. ODSE/ODPE oc-curs in anisotropic crystals[14–18] and artificially tilted multilay-ers (ATMLs),[19–34] which consist of two conductors alternatelyand obliquely stacked. Recently, hybridization of the multipletransverse thermoelectric effects in ATMLs has been demon-strated as a promising approach for the realization of giant trans-verse thermoelectric conversion.[32,33] Combining ODSE withONE/ANE can provide improved thermoelectric performance be-yond what can be achieved with ONE/ANE alone.[32,33] How-ever, this approach typically requires the application of an ex-ternal magnetic field to drive ONE/ANE, limiting practical ap-plications. Although ANE can occur in the absence of a mag-netic field in hard magnetic materials, in previous studies, ei-ther soft magnetic materials were used or the remanent mag-netization direction in permanent-magnet-based ATMLs did notsatisfy the symmetry of ANE; hybridization of ANE in ATMLsin the absence of a magnetic field has not been achieved sofar.[32–34] Additionally, the experimentally determined transversethermoelectric figure of merit in ATMLs remains below 0.20due to unoptimized ODSE and/or performance degradation dueAnn. Phys. (Berlin) 2025, 537, e00127 e00127 (1 of 9) © 2025 The Author(s). Annalen der Physik published by Wiley-VCH GmbHhttp://www.ann-phys.orgmailto:ANDO.Fuyuki@nims.go.jpmailto:UCHIDA.Kenichi@nims.go.jphttps://doi.org/10.1002/andp.202500127http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fandp.202500127&domain=pdf&date_stamp=2025-06-29www.advancedsciencenews.com www.ann-phys.orgFigure 1. Schematic illustration of transverse thermoelectric conversionin an artificially tilted multilayer (ATML) composed of magnetic and ther-moelectric materials. The magnetic materials used in this study, theSmCo5 slabs, have the large anisotropy with an in-plane magnetic easyaxis. The heat current Jq flows along the y direction, generating a chargecurrent Jc along the x direction. The off-diagonal Seebeck effect (ODSE)arises from the ATML structure with the tilt angle 𝜃, while the anomalousNernst effect (ANE) occurs depending on themagnetizationM in themag-netic materials.to interfacial electrical/thermal resistances.[34] Addressing thesechallenges requires materials and structural designs that effec-tively exploit hybrid transverse thermoelectric conversion at zerofield.[35–37]The effectiveness of the hybrid transverse thermoelectric con-version can be found in the figure of merit zxyT (= Sxy2𝜎xxT/𝜅yy),where Sxy, 𝜎xx, and 𝜅yy respectively denote the transverse ther-mopower, electrical conductivity along the x direction, and ther-mal conductivity along the y direction for ATML. According toRef. [33], for ANE-hybridized ATML systems, the total transversethermopower consists of the contributions fromODSE and ANE:Sxy = SODSE + ŜANE and zxyT ∝ Sxy2 = SODSE2 + 2SODSEŜANE +ŜANE2. Here, SODSE represents the transverse thermopower due toODSE and ŜANE is the effective anomalousNernst coefficient con-sidering the reduction due to the shunting effect. The key point isthat the hybridization of ODSE and ANE generates the additional2SODSEŜANE term, leading to a larger ANE-induced zxyT enhance-ment than what ANE alone can achieve, especially when ODSE islarge. This explains why our ATMLs are fundamentally designedto optimize ODSE.In this study, we demonstrate high-performance transversethermoelectric conversion based on the hybridization of ODSEand ANE in ATML at zero field (Figure 1). Using a lock-inthermography (LIT) method, we directly observe a temperaturemodulation through the transverse thermoelectric conversionand clarify the contributions from the reciprocal effects of ODSEand ANE independently. The enhancement of the transversethermoelectric performance is quantified by direct transversethermopower measurements; the transverse figure of meritfor our ATML reaches ≈0.3 at room temperature owing to thelarge ODSE contribution and the superposition of the ANEcontribution.2. Experimental SectionThis study used ATML consisting of SmCo5-type permanentmagnets exhibiting large ANE[9,11] and Bi0.2Sb1.8Te3 thermoelec-tric materials exhibiting the large Seebeck effect. This ATML wassimilar to that used in Ref. [34] and known to exhibit large ODSE.However, the magnetization direction of the SmCo5 slabs in theATML was different from that in the previous system. Althoughthe magnetic easy axis of the SmCo5 slabs in the previous sys-tem was perpendicular to the stacking plane, the SmCo5 slabsused in this study have the easy axis along the in-plane direction.Thus, in the configuration depicted in Figure 1 where a tempera-ture gradient was applied in the y direction, both ODSE and ANEcould generate a charge current in the x direction.[33] Owing tothe large remanent magnetization and coercivity of the SmCo5slabs, the ATML enables the utilization of ANE without applyingan external magnetic field.The SmCo5/Bi0.2Sb1.8Te3-based ATML was prepared as fol-lows. The SmCo5 slabs (available from Magfine Corporation,Japan) and BiSbTe alloy powders (available from Toshima Manu-facturing Co., Ltd.) were alternately stacked and bonded by sparkplasma sintering under a pressure of 30 MPa at 450 °C for 30min. The SmCo5 slabs were used as delivered without additionalprocessing. The sintered multilayer stack was cut into rectangu-lar shapes with a tile angle of 25° for LIT measurements (≈10.0× 2.0 × 2.0 mm3) and thermopower measurements (13.5 × 10.3× 1.0 mm3). Note that zxyT was evaluated using the latter sampleemployed for the thermopowermeasurements. The tilt angle wasdetermined by the method described later. Then, the magnetiza-tion of the rectangular samples was aligned along the magneticeasy axis at room temperature using a superconducting mag-net. The composition of the SmCo5 slabs was confirmed to bestoichiometric through inductively coupled plasma analysis. Thecomposition of the Bi0.2Sb1.8Te3 slabs prepared under the samesintering condition was confirmed in the previous study.[34] Elec-tron backscatter diffraction (EBSD) analysis was conducted us-ing a Crossbeam 550 instrument (Carl Zeiss AG) equipped withan EBSD detector. The SmCo5 slabs for EBSD analysis were pre-pared by mechanical polishing.The LIT method was used to directly measure the transversethermoelectric conversion in SmCo5/Bi0.2Sb1.8Te3-based ATML.The LIT method is an infrared thermometry technique that en-ables visualization of the spatial distribution and temporal re-sponse of temperature modulation induced by an applied chargecurrent with high temperature and spatial resolutions.[38–40] Inthe LIT measurements, heating and cooling signals oscillating atthe same frequency as the applied periodic charge current werecaptured as thermal images. The LIT measurements were per-formed by applying a square-wave-modulated ac charge currentwith an amplitude of 1 A, frequency f range of 0.1–10.0 Hz, andzero offset to the sample along its longitudinal direction (x direc-tion in Figure 1). The resulting thermal images were convertedinto lock-in amplitude A and phase ϕ images through Fourieranalysis. By extracting the first harmonic component of these im-ages, the contribution of the thermoelectric effects (∝Jc, whereJc is the amplitude of Jc) could be distinguished from that ofAnn. Phys. (Berlin) 2025, 537, e00127 e00127 (2 of 9) © 2025 The Author(s). Annalen der Physik published by Wiley-VCH GmbH 15213889, 2025, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/andp.202500127 by National Institute For, Wiley Online Library on [11/08/2025]. 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.ann-phys.orgwww.advancedsciencenews.com www.ann-phys.orgFigure 2. Experimental setup and measurement configuration. a) Photograph of the superconducting magnet used to apply a magnetic field.SmCo5/Bi0.2Sb1.8Te3-based ATML is mounted at the center of the bore using a custom sample holder. b) Enlarged view of the sample holder show-ing the SmCo5/Bi0.2Sb1.8Te3-based ATML fixed on Al blocks. A chip heater was placed to generate a temperature gradient across the ATML. T-typethermocouples were attached to both Al blocks to measure the temperature difference, and two sensing wires were bonded to the surface to measurethe thermoelectric voltage.Joule heating (∝Jc2). This process allows for the selective visu-alization of thermoelectric effects, such as the Peltier effect andanomalous Ettingshausen effect.[41,42] The A image representsthe magnitude of the temperature modulation and the ϕ imageprovides information on the sign of the temperature modulationand the time delay due to thermal diffusion, helping to clarify thetransverse thermoelectric conversion mechanism in ATMLs.[32]All LIT measurements were performed using Enhanced Lock-In Thermal Emission (ELITE, DCG Systems G.K.) at room tem-perature and atmospheric pressure.The LITmeasurements wereconducted in two configurations: cross-section configuration andtop-side configuration (see Section 3.2). For measurements in-volving different magnetization states, the sample was magne-tized in a separate superconducting magnet and then re-insertedinto the LIT setup. The thermal images were aligned from suc-cessive runs by shifting them so that the SmCo5/Bi0.2Sb1.8Te3 in-terface positions overlapped, thus correcting for any slight mis-alignment.The anomalous Nernst coefficient of SmCo5 was also esti-mated using the LIT method. The LIT method enables the quan-titative measurements of the temperature modulation inducedby AEE; through the estimated anomalous Ettingshausen coeffi-cient and the Onsager reciprocal relation, the anomalous Nernstcoefficient can be determined.[9]For the direct Sxy measurements, the samplewas fixed betweentwo anodized Al blocks. One block was connected to a heat bathwhile the other incorporated a chip heater, generating a temper-ature gradient ∇T across the sample. The surface of the samplewas coated with black ink and the magnitude of ∇T was mea-sured with the infrared camera. Sxy was determined by measur-ing the DC voltage between two Al-1%Si wires directly attachedto the sample surface. The wires spanned two SmCo5 layers andthree Bi0.2Sb1.8Te3 layers, ensuring that the measured Sxy repre-sents an average across multiple layers. A photograph of the ac-tual sample and experimental setup is provided in Figure 2 to il-lustrate the measurement configuration. To determine 𝜎xx, four-terminal resistance measurements were carried out for the samesample. Cu wires were connected to the side surfaces of the sam-ple, which had been coated with solder using ultrasonic solderingto ensure uniform current injection. An ac charge current withan amplitude of 10 mA was applied using a battery internal resis-tance tester (BT3562, Hioki E.E. Corp.) while measuring 𝜎xx. AllSxy and 𝜎xx measurements were performed at room temperatureand atmospheric pressure.3. Results and Discussion3.1. Structural Optimization and Simulation of TransverseThermoelectric PerformanceTo evaluate and optimize the transverse thermoelectric perfor-mance of ATML, we first measured the transport properties ofthe constituent materials, SmCo5 and Bi0.2Sb1.8Te3. The resultsare summarized in Table 1. The SmCo5 slab used in this studyexhibited a thermal conductivity 𝜅 of 12.7 ± 0.3 W m−1 K−1 andelectrical conductivity 𝜎 of 1.91 × 106 S m−1, while the previoussample showed higher 𝜅 of 16.8± 0.5Wm−1 K−1 and comparable𝜎 of 1.80× 106 Sm−1.[34] The reduced 𝜅 is expected to increase thefigure of merit zxyT for ATML. The anomalous Nernst coefficientof SmCo5 used in this study was found to be 2.9 μV K−1, whichis slightly smaller than but consistent with the value reported inthe previous studies.[9,11,36]To investigate the origin of the difference in 𝜅, we analyzedthe microstructure of the SmCo5 slabs using EBSD. Figure 3Table 1. Transport properties of SmCo5 andBi0.2Sb1.8Te3 used in this study.Material 𝜎 [106 S m−1] 𝜅 [W m−1 K−1] S [μV K−1]SmCo5 1.91 12.7 −19.78Bi0.2Sb1.8Te3 0.121 1.00 177.9Ann. Phys. (Berlin) 2025, 537, e00127 e00127 (3 of 9) © 2025 The Author(s). Annalen der Physik published by Wiley-VCH GmbH 15213889, 2025, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/andp.202500127 by National Institute For, Wiley Online Library on [11/08/2025]. 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.ann-phys.orgwww.advancedsciencenews.com www.ann-phys.orgFigure 3. Electron backscatter diffraction analysis showing inverse pole figure maps of the SmCo5 grains and grain size distributions of the SmCo5 slabswith a) in-plane magnetic easy axis and b) out-of-plane magnetic easy axis. The direction of the magnetic easy axis is indicated by the white symbol atthe top-left of each image. davg and SD denote the average grain size and standard deviation, respectively.presents the results of the EBSD analysis showing inverse polefigure maps of the SmCo5 grains and grain size distributions forthe SmCo5 slab with the in-plane magnetic easy axis used in thisstudy (Figure 3a) and that with the out-of-plane magnetic easyaxis used in the previous study (Figure 3b). The SmCo5 slab usedin this study exhibits a smaller average grain size (11.6 μm) anda narrower grain size distribution compared to the previously re-ported sample (13.5 μm). These microstructural differences canbe one of the possible reasons for the reduced 𝜅 observed in thepresent sample.[43,44] While a systematic study of how grain sizeaffects the thermal conductivity of SmCo5 would be insightful, itlies beyond the scope of this work and is proposed as a directionfor future research. Note that EBSD provides crystallographic ori-entation and grain size information, but does not probe mag-netic domains; accordingly, our analysis focused on the crystallo-graphic features, and the magnetic easy axis of the SmCo5 slabswas predetermined by the supplier.Using 𝜎, 𝜅, and the Seebeck coefficient S of SmCo5 andBi0.2Sb1.8Te3, the transport properties of SmCo5/Bi0.2Sb1.8Te3-based ATML were simulated based on the methods of thereferences.[23,30] Figure 4 shows the contour maps of 𝜎xx, 𝜅yy, Sxy,and zxyT at T= 300 K as functions of the tilt angle 𝜃 and thicknessratio t= tSmCo/(tSmCo+tBST), where tSmCo(BST) is the thickness of theSmCo5 (Bi0.2Sb1.8Te3) layer. The optimized zxyT value for ODSEin SmCo5/Bi0.2Sb1.8Te3-based ATML reaches 0.30 at room tem-peraturewhen 𝜃 = 25° and t= 0.50. This significant improvementof zxyT compared to that reported in Ref. [34] is attributed mainlyto the aforementioned difference in the transport properties ofthe SmCo5 slabs. SmCo5/Bi0.2Sb1.8Te3-based ATMLwas designedand synthesized to optimize ODSE based on the calculation re-sult. The experimentally realized 𝜃 and t of SmCo5/Bi0.2Sb1.8Te3-based ATMLwere estimated to be 25± 2° and 0.41± 0.02, respec-tively. The individual thicknesses of the SmCo5 and Bi0.2Sb1.8Te3layers were 0.476 ± 0.017 mm and 0.691 ± 0.066 mm. The tiltangle and thickness ratio were determined from real-space im-ages acquired by an infrared camera, with a spatial resolution of15 μm per pixel. The corresponding zxyT value was calculated tobe 0.29, showing that SmCo5/Bi0.2Sb1.8Te3-based ATML with al-most optimized zxyT was synthesized, as shown by red points inFigure 4.3.2. Observation of Giant Off-Diagonal Peltier EffectHere, we visualize the ODPE and AEE signals as temperaturemodulation in the following LIT measurements, whereas theODSE and ANE signals shown in Section 3.4 are measured sep-arately as transverse voltages. Figure 5 displays the results of theLITmeasurements for demagnetized SmCo5/Bi0.2Sb1.8Te3-basedATML. The A and ϕ images at different lock-in frequencies (f= 10.0, 1.0, and 0.1 Hz) in the cross-section configuration areshown in Figure 5a,b. At f = 10.0 Hz, heating and cooling signalsare localized near the junction interfaces between SmCo5 andBi0.2Sb1.8Te3, where the A signals peak along the oblique inter-faces (Figure 5c) and the ϕ image exhibits a 180° phase reversalbetween neighboring interfaces (Figure 5d), consistent withPeltier-effect-induced temperature modulation as previouslyreported in similar ATML systems.[32–34] Unlike conventionalAnn. Phys. (Berlin) 2025, 537, e00127 e00127 (4 of 9) © 2025 The Author(s). Annalen der Physik published by Wiley-VCH GmbH 15213889, 2025, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/andp.202500127 by National Institute For, Wiley Online Library on [11/08/2025]. 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.ann-phys.orgwww.advancedsciencenews.com www.ann-phys.orgFigure 4. Contour maps of the transport properties as functions of the tilt angle 𝜃 and thickness ratio t in SmCo5/Bi0.2Sb1.8Te3-based ATML at 300 K:a) electrical conductivity along the x direction 𝜎xx, b) thermal conductivity along the y direction 𝜅yy, c) transverse thermopower Sxy, and d) transversefigure of merit zxyT. The red points correspond to the 𝜃 and t values for the sample used in this study, i.e., 𝜃 = 25° and t = 0.41.Peltier-effect-induced temperature modulation at non-obliqueinterfaces,[45,46] the magnitude of the A signals is non-uniformalong the oblique interfaces due to the non-uniform Jc flowwithin the ATML structure, confirming the transverse thermo-electric conversion originating from ODPE. As f decreases to 0.1Hz, approaching a nearly steady-state, thermal diffusion broad-ens the heating and cooling signals. The ϕ signals range from≈0° (lower side of the sample) to 180° (upper side of the sample)in the direction perpendicular to Jc, indicating transverse ther-moelectric heating and cooling induced by ODPE, respectively.The x-directional profiles ofA and ϕ further reveal periodic varia-tions due to the multilayer structure (Figure 5e,f). The transversethermoelectric cooling behavior is more distinctly observed inthe top-side configuration, as demonstrated in Figure 5i–p.To estimate the transverse thermoelectric heating and cool-ing performance of SmCo5/Bi0.2Sb1.8Te3-based ATML, the LITresults were averaged over one SmCo5/Bi0.2Sb1.8Te3 unit.Figure 5g,h (5o,p) shows the f dependence of the averaged A andϕ values, i.e., Aave and ϕave, for one SmCo5/Bi0.2Sb1.8Te3 unit inthe cross-section (top-side) configuration. The corresponding av-eraged areas are defined by the white rectangles in Figure 5c,d(5k,l). The magnitude of Aave monotonically increases as f de-creases while ϕave gradually shifts toward 180°, approaching thesteady-state temperature distribution. Notably, the Aave value at f= 0.1 Hz for present SmCo5/Bi0.2Sb1.8Te3-based ATML is over 10times (≈1.5 times) larger than that of Nd2Fe14B/Bi88Sb12-basedATML (conventional SmCo5/Bi0.2Sb1.8Te3-based ATML) used inthe previous studies.[32,34] These observations provide direct evi-dence that present SmCo5/Bi0.2Sb1.8Te3-based ATML exhibits en-hanced transverse thermoelectric performance due to its opti-mized material and structural design, further confirming its su-periority over previously reported ATML systems.3.3. Separation of Anomalous Ettingshausen Effect fromOff-Diagonal Peltier EffectNext, we separately visualize the contributions of ODPE and AEEin magnetized SmCo5/Bi0.2Sb1.8Te3-based ATML. To magnetizethe SmCo5 layers, the magnetic field 𝜇0H = ±5.0 T, where 𝜇0 andH are the vacuum permeability and magnitude of the magneticfield, respectively, was applied along the z direction (Figure 1)before the LIT measurements (note that 5.0 T is larger thanthe coercivity of the SmCo5 slabs). The magnetization (M)-even-dependent component represents temperature modulation thatdoes not changewith theM reversal, such asODPE and itsmodu-lation by theH and/orM dependence of 𝜎, 𝜅, and S, while theM-odd-dependent component captures effects that change with theM reversal, characteristic of AEE. To separate the ODPE and AEEcontributions, theM-even- andM-odd-dependent components ofthe LIT signals were extracted using the following equations:Aeven = |||A (+M) e−i𝜙(+M) + A (−M) e−i𝜙(−M)||| ∕2 (1)𝜙even = − arg[A (+M) e−i𝜙(+M) + A (−M) e−i𝜙(−M)] (2)Aodd =|||A (+M) e−i𝜙(+M) − A (−M) e−i𝜙(−M)||| ∕2 (3)𝜙odd = − arg[A (+M) e−i𝜙(+M) − A (−M) e−i𝜙(−M)] (4)Ann. Phys. (Berlin) 2025, 537, e00127 e00127 (5 of 9) © 2025 The Author(s). Annalen der Physik published by Wiley-VCH GmbH 15213889, 2025, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/andp.202500127 by National Institute For, Wiley Online Library on [11/08/2025]. 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.ann-phys.orgwww.advancedsciencenews.com www.ann-phys.orgFigure 5. Transverse thermoelectric conversion in demagnetized SmCo5/Bi0.2Sb1.8Te3-based ATML. a) Schematic of the sample structure in the cross-section configuration. b) Steady-state temperature image during the LIT measurement in the cross-section configuration. c,d) Lock-in amplitude A (c)and phase ϕ (d) images at the lock-in frequencies of f = 10.0, 1.0, and 0.1 Hz. e,f) x-directional A (e) and ϕ (f) profiles along the white dotted lines in thetop panels of c and d, respectively. g,h) f dependence of the averaged lock-in amplitude Aave (g) and phase ϕave (h) values over one SmCo5/Bi0.2Sb1.8Te3unit. i–p) Results for the top-side configuration. The Aave and ϕave values in g and h (o and p) were estimated by averaging A and ϕ signals in the areasdefined by the white rectangles in c and d (k and l), corresponding to the gray shaded area in e and f (m and n), respectively. In all the LIT measurements,a square-wave-modulated ac charge current with an amplitude of 1 A and zero offset was applied.whereAeven (Aodd) andϕeven (ϕodd) represent the lock-in amplitudeand phase exhibiting the M-even (M-odd) dependence. A(+M)[ϕ(+M)] and A(−M) [ϕ(−M)] are defined as A (ϕ) measured whenthe magnetization vector M is along the +z and −z directions,respectively. Importantly, no external magnetic field was appliedduring the LIT measurements, meaning that AEE occurs due tothe remanent magnetization of the SmCo5 slabs.Figure 6a,b shows the Aeven and ϕeven images at different f val-ues (10.0, 1.0, and 0.1 Hz) in the top-side configuration. The pe-riodic heating and cooling signals along the multilayer interfacesconfirm the presence of ODPE, consistent with Figure 5. Themagnitude of the Aeven signals were found to be comparable tothose observed in the demagnetized sample, confirming the mi-nor role of the magnetoresistance, magneto-thermal resistance,and magneto-Peltier effect in the ODPE signals.The M-odd-dependent component, which isolates the AEEcontribution, is shown in Figure 6e,f. The temperature distri-bution localized in the SmCo5 regions defined by the gray rect-angle at f = 10.0 Hz confirms the existence of the AEE contri-bution in SmCo5 even in the absence of an applied magneticfield. The f dependence of Aodd (Figure 6g) shows an increas-ing trend at lower f, similar to the ODPE case, while the ϕodd(Figure 6h) remains close to 180°, indicating that the transversethermoelectric cooling also occurs in theM-odd-dependent com-ponent. A substantial magnitude of Aodd was also observed in theBi0.2Sb1.8Te3 regions defined by the orange rectangle. However,the Aodd signals at f = 10 Hz is strongly localized in the SmCo5regions, while ϕodd in the Bi0.2Sb1.8Te3 regions gradually shiftstoward 180° as f decreases. This suggests that the Bi0.2Sb1.8Te3do not act as an independent heat source and the observed Aoddsignals in the Bi0.2Sb1.8Te3 regions arise primarily from heat dif-fusion driven by AEE in the SmCo5 regions. Because all LITmea-surements in this study were performed in the absence of anexternal magnetic field, the contribution of the ordinary Etting-shausen effect in the Bi0.2Sb1.8Te3 is negligible under the presentconditions. These clear observations of both ODPE and AEEwithout an external magnetic field highlight a significant advan-tage of in-plane magnetized SmCo5/Bi0.2Sb1.8Te3-based ATMLover previous systems that required an external magnetic field toinduce ANE.Ann. Phys. (Berlin) 2025, 537, e00127 e00127 (6 of 9) © 2025 The Author(s). Annalen der Physik published by Wiley-VCH GmbH 15213889, 2025, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/andp.202500127 by National Institute For, Wiley Online Library on [11/08/2025]. 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.ann-phys.orgwww.advancedsciencenews.com www.ann-phys.orgFigure 6. Contributions of ODPE and AEE in SmCo5/Bi0.2Sb1.8Te3-based ATML in the top-side configuration. a,b)M-even-dependent component of thelock-in amplitude Aeven (a) and phase ϕeven (b) images at f = 10.0, 1.0, and 0.1 Hz. c,d) f dependence of Aeven (c) and ϕeven (d). e–h) Results for theM-odd-dependent component: Aodd and ϕodd. Themagnetic field with 𝜇0H=±5.0 T was applied along the z direction (Figure 1) tomagnetize the samplebefore the LIT measurements. 𝜇0 andM represent the vacuum permeability and spontaneous magnetization of the SmCo5-type magnets, respectively.The data points in c and d (g and h) were obtained by averaging Aeven and ϕeven (Aodd and ϕodd) signals in the areas defined by the gray and orangerectangles in a and b (e and f), respectively. All the LIT data in this figure were measured in the absence of an external magnetic field.3.4. Performance of Hybrid Transverse ThermoelectricConversionTo investigate the total transverse thermoelectric performance inSmCo5/Bi0.2Sb1.8Te3-based ATML, we experimentally measured𝜎xx and Sxy and determined zxyT. A crucial factor of complex ther-moelectric materials is the interfacial resistance between con-stituent layers, which can significantly impact transport prop-erties. However, as reported in the previous report,[34] the in-terfacial electrical and thermal resistances between SmCo5 andBi0.2Sb1.8Te3 were found to be negligible, confirming that thetwo materials are well bonded without significant interfacial re-sistances. Furthermore, magnetic property measurements con-firmed that the SmCo5 layers retained their permanent magnetcharacteristics even after sinter-bonding with Bi0.2Sb1.8Te3. TheSmCo5 layers exhibited a large remanent magnetization of 0.84T and coercivity of 2.95 T, as shown in the top panel of Figure 7a.This result ensures that SmCo5/Bi0.2Sb1.8Te-based ATML func-tions as a permanent magnet, enabling magnetic-field-free hy-brid transverse thermoelectric operation.For a precise assessment of the thermoelectric performancearising from the hybrid action of ODSE and ANE, we applied atemperature difference ΔT between the top and bottom surfacesof ATML and measured the transverse thermoelectric voltageV under an external magnetic field with 𝜇0H = ±5.0 T, asshown in the inset of Figure 7b. The magnetization curve inthe top panel of Figure 7a and the H dependence of V in thebottom panel of Figure 7a exhibit a similar trend, confirming thecorrelation between the magnetic and thermoelectric responses.The transverse thermoelectric voltage follows the hystereticbehavior of magnetization, demonstrating the presence of theANE-induced transverse thermoelectric output that changeswith magnetization reversal. The V-H curves in the bottompanel of Figure 7a also exhibit the symmetric contribution withrespect to H; this can be explained by the M-even-dependentcomponent, such as the magnetoresistance, magneto-thermalresistance, and magneto-Peltier effect, superimposed on thetransverse thermoelectric conversion.The thermopower measurements in Figure 7b determine Sxyto be−70.7± 0.6 μV K−1 (−72.1± 0.6 μV K−1) at 0 T after aligningM along the+z (−z) direction, which is represented by+M (−M).Interestingly, the experimentally obtained values of Sxy exceededthe calculated value of−65.5 μVK−1, likely due to the contributionof off-diagonal thermal conduction in the adiabatic condition,consistent with observations in a previous report.[47] In addition,wemeasured the ac resistance of ATML, obtaining a value of 1.46mΩ, which was slightly higher than the calculated resistance of1.23 mΩ from the simulated 𝜎xx and the sample geometry. Usingthis measured resistance, we determined 𝜎xx of the sample. Theslightly lower 𝜎xx may be attributed to microstructural factorssuch as cracks introduced in SmCo5 during the sintering process.Based on the measured 𝜎xx and Sxy values and simulated 𝜅yy, weestimated zxyT to be 0.288± 0.005 at+M and 0.299± 0.005 at−M.Although the difference in zxyT between the +M and −M config-urations appears modest, it is important that this variation origi-nates from ANE. The resulting 3.9% change in zxyT, correspond-ing to an increase of 0.011, is significantly larger than the figureof merit of ANE alone for SmCo5, which is smaller than 0.001 atroom temperature. This clearly demonstrates that the cross term2SODSEŜANE, introduced by the hybridization of ODSE and ANE,plays a crucial role in enhancing the overall transverse thermo-electric performance. Despite the lower 𝜎xx, the higher measuredSxy compensated for this reduction, resulting in the zxyT valuescomparable to the analytical prediction in Figure 4d. Most impor-tantly, this experimentally evaluated zxyT value reaching≈0.3 rep-resents a record-high performance for transverse thermoelectricAnn. Phys. (Berlin) 2025, 537, e00127 e00127 (7 of 9) © 2025 The Author(s). Annalen der Physik published by Wiley-VCH GmbH 15213889, 2025, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/andp.202500127 by National Institute For, Wiley Online Library on [11/08/2025]. 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.ann-phys.orgwww.advancedsciencenews.com www.ann-phys.orgFigure 7. Hybrid transverse thermoelectric generation in SmCo5/Bi0.2Sb1.8Te3-based ATML. a) H dependence of the magnetization M of the SmCo5-type magnets (top panel of a) and transverse thermoelectric voltage V at various ΔT values (bottom panel of a). The M-H curve was measured byvibrating sample magnetometry. ΔT denotes the temperature difference between the top and bottom surfaces of the sample. b) Temperature gradient∇T dependence of the transverse electric field E. The transverse thermopower Sxy was estimated to be −70.7 μV K−1 (−72.1 μV K−1) at 0 T after aligningM along the +z (−z) direction, which is represented by +M (−M). The inset shows a schematic of the setup for measuring the transverse thermopower.conversion around room temperature, surpassing previouslyreported values for transverse thermoelectric materials.[34]4. ConclusionWe demonstrated a high-performance, magnetic-field-free hybrid transverse thermoelectric conversion usingSmCo5/Bi0.2Sb1.8Te3-based ATMLs. By leveraging the spon-taneous magnetization of SmCo5, we successfully induced ANEin ATML without applying an external magnetic field. ThroughLIT measurements and direct thermoelectric property char-acterization, we observed enhanced transverse thermoelectricperformance driven by the hybridization of ODSE and ANE.Although ODSE dominates the overall output, ANE introduces amagnetization-direction-dependent component, enabling mag-netically switchable thermoelectric conversion. This switchablefunctionality, coupled with the intrinsic performance enhance-ment from hybridization, adds a valuable degree of control forfuture applications of transverse thermoelectrics. The optimizedATML structure exhibited a transverse figure of merit zxyTof ≈0.3 at room temperature, setting a new benchmark forhybrid transverse thermoelectric materials. Our results high-light the potential of ATMLs comprising permanent magnetsas a promising platform for energy harvesting and thermalmanagement applications, particularly in scenarios requiringstable, high-performance thermoelectric conversion withoutcontinuous magnetic field application. Future work shouldfocus on finding and developing permanent magnets with giantANE as well as further improving the performance of ODSEthrough the optimization of material combination, composition,microstructural design, and interface structures.AcknowledgementsThe authors thank K. Suzuki and M. Isomura for technical support. Thiswork was supported by ERATO “Magnetic Thermal Management Materi-als” (No. JPMJER2201) from Japan Science and Technology Agency (JST)and Grant-in-Aid for Early-Career Scientists (KAKENHI) (No. 24K17610)from Japan Society for the Promotion of Science (JSPS).Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from the cor-responding author upon reasonable request.Keywordsanomalous Nernst effect, artificially tilted multilayer, off-diagonal Seebeckeffect, permanent magnet, transverse thermoelectricsReceived: March 28, 2025Revised: June 15, 2025Published online: June 29, 2025[1] D. M. Rowe, Thermoelectrics Handbook: Macro to Nano, CRC Press,New York, USA, 2006.[2] L. E. Bell, Science 2008, 321, 1457.[3] G. J. Snyder, E. S. Toberer, Nat. Mater. 2008, 7, 105.Ann. Phys. (Berlin) 2025, 537, e00127 e00127 (8 of 9) © 2025 The Author(s). 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Annalen der Physik published by Wiley-VCH GmbH 15213889, 2025, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/andp.202500127 by National Institute For, Wiley Online Library on [11/08/2025]. 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.ann-phys.org Zero-Field Hybridization of Anomalous Nernst and Off-diagonal Seebeck Effects in Artificially Tilted Multilayers 1. Introduction 2. Experimental Section 3. Results and Discussion 3.1. Structural Optimization and Simulation of Transverse Thermoelectric Performance 3.2. Observation of Giant Off-Diagonal Peltier Effect 3.3. Separation of Anomalous Ettingshausen Effect from Off-Diagonal Peltier Effect 3.4. Performance of Hybrid Transverse Thermoelectric Conversion 4. Conclusion Acknowledgements Conflict of Interest Data Availability Statement Keywords