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[Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), [Fuyuki Ando](https://orcid.org/0009-0003-7789-8170), [Hossein Sepehri-Amin](https://orcid.org/0000-0002-7856-7897), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051)

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[Hybridizing anomalous Nernst effect in artificially tilted multilayer based on magnetic topological material](https://mdr.nims.go.jp/datasets/171c5afc-4446-4a73-8ba1-e70740a6195b)

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Hybridizing anomalous Nernst effect in artificially tilted multilayer based on magnetic topological materialArticle https://doi.org/10.1038/s41467-024-53723-2Hybridizing anomalous Nernst effect inartificially tilted multilayer based onmagnetic topological materialTakamasa Hirai 1 , Fuyuki Ando 1, Hossein Sepehri-Amin 1 &Ken-ichi Uchida 1,2Transverse thermoelectric conversion holds significant potential in addressingcomplex challenges faced by classical Seebeck/Peltier modules. A promisingtransverse thermoelectric phenomenon is the anomalous Nernst effect origi-nating from nontrivial band structures in magnetic topological materials.However, the currently reported performance of the anomalous Nernst effectin topological materials, e.g., Co2MnGa, remains insufficient for practicalthermoelectric applications. Here, we unveil an unconventional availability ofthe anomalous Nernst effect by integrating magnetic topological materialsinto artificially tilted multilayers, known to exhibit the structure-inducedtransverse thermoelectric conversion due to the off-diagonal Seebeck effect.Our experiments reveal that the transverse thermoelectric performance inCo2MnGa-based artificially tilted multilayers is improved through the hybridaction of the anomalous Nernst and off-diagonal Seebeck effects, with themagnetization-dependent performance modulation being one order of mag-nitude greater than the performance achievable with the anomalous Nernsteffect alone. This synergy underscores the importance of hybrid transversethermoelectric conversion and paves a way for advancing thermoelectricapplications using magnetic materials.Developments in thermoelectric technologies have garnered atten-tion for their capability to directly convert a heat current Jq into acharge current Jc and vice versa, enabling power generation fromwasted/environmental heat and solid-state refrigeration withoutmechanical moving parts1–4. Conventional thermoelectric devices arebased on the Seebeck effect and its Onsager reciprocal, that is, thePeltier effect, in which Jc and Jq flow in the same direction. Due to thislongitudinal geometry, a thermoelectric module based on the See-beck/Peltier effect usually consists of a bunch of p-type and n-typeconductors connected electrically in series and thermally in parallelwithmany electrodes to enlarge the thermoelectric output. Althoughthe Seebeck/Peltier module is progressing to the daily market, itscomplex three-dimensional structure remains indispensable pro-blems, e.g., low mechanical endurance and energy loss due to manyelectrode junctions and their contact electrical and thermalresistances.Transverse thermoelectric conversion has practical advantagesover longitudinal thermoelectric effects4. The transverse thermo-electric effects allow interconversion between Jc and Jq in the ortho-gonal direction. Separating the Jc and Jq directions enables theenhancement of thermoelectric output simply by upscaling the size ofa single thermoelectric material, which can reduce the number ofelectrodes and junctions in modules4. The ordinary Nernst effect(ONE) is a representative transverse thermoelectric effect; it is usuallyobtained in nonmagnetic conductors under an external magnetic fieldH, referring to the generation of Jc in the cross-product direction of theapplied Jq and H owing to the Lorentz force. The ordinary Etting-shausen effect (OEE) is the Onsager reciprocal of ONE. In magneticReceived: 29 May 2024Accepted: 21 October 2024Check for updates1National Institute for Materials Science, Tsukuba 305-0047, Japan. 2Department of Advanced Materials Science, Graduate School of Frontier Sciences, TheUniversity of Tokyo, Kashiwa 277-8561, Japan. e-mail: HIRAI.Takamasa@nims.go.jp; UCHIDA.Kenichi@nims.go.jpNature Communications |         (2024) 15:9643 11234567890():,;1234567890():,;http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-5577-8018http://orcid.org/0000-0002-5577-8018http://orcid.org/0009-0003-7789-8170http://orcid.org/0009-0003-7789-8170http://orcid.org/0009-0003-7789-8170http://orcid.org/0009-0003-7789-8170http://orcid.org/0009-0003-7789-8170http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-53723-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-53723-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-53723-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-53723-2&domain=pdfmailto:HIRAI.Takamasa@nims.go.jpmailto:UCHIDA.Kenichi@nims.go.jpwww.nature.com/naturecommunicationsmaterials, the anomalous Nernst (Ettingshausen) effect manifests viathe momentum-space Berry curvature related to the spin-orbit inter-action and/or spin-dependent scattering acting on conduction car-riers, where Jc (Jq) is generated in the cross-product direction of theapplied Jq (Jc) and a spontaneousmagnetizationM, which is referred toas ANE (AEE)5,6. Unlike ONE/OEE, which requires a substantial magni-tude ofH to generate a large transverse thermopower, ANE/AEE offersan advantage of operating at much smaller magnetic field values or inthe absence of H when magnetic materials have finite remanentmagnetization. Such features and functionalities provided by ANE/AEEhave motivated advanced research on spin caloritronics and con-densed matter physics7–14. While ONE has been shown to scale withcarrier mobility15, such simple scaling rules do not exist for ANE, andthe material exploration for ANE is underway from various perspec-tives. By spotlighting the intrinsicBerry curvaturecontribution, severalpromising magnetic topological materials for transverse thermo-electrics have been discovered16–25. However, the thermopower due toANE is still < 8μV/K and the record-high dimensionless figure of meritzT for ANE is approximately 7 × 10−4 at the temperature T ~ 300 K26,which is several orders of magnitude smaller than that for the Seebeckeffect.In this study, we provide a novel practical possibility for ANE/AEEin transverse thermoelectrics by hybridizing it into artificially tiltedmultilayers (ATMLs). The transverse thermoelectric conversion is not aunique feature of the Nernst/Ettingshausen effects but appears inanisotropic materials without requiring H orM. ATML is one exampleof such anisotropic materials and consists of alternately and obliquelystacked two different conductors27–36. The geometrically tilted struc-ture generates finite off-diagonal components in the thermoelectrictransport tensors owing to anisotropic carrier flows; thus, it is usuallycalled the off-diagonal Seebeck/Peltier effect (ODSE/ODPE). Here, thesign of the thermoelectric output due to ODSE/ODPE can be reversedby the 180° reversal of the relative angle between the tilting directionand input heat/charge current. Because the origin ofODSE/ODPE is theSeebeck/Peltier coefficients of constituentmaterials, a large transverseconversion by ODSE/ODPE has been realized using conventionalthermoelectric materials27–36. Herein, we report hybrid transversemagneto-thermoelectric conversion by superimposing ANE/AEE onODSE/ODPE in ATMLs consisting of magnetic topological material/thermoelectric material stacks (Fig. 1). Although the hybrid transversemagneto-thermoelectric conversion based on ONE/OEE and ODSE/ODPE in ATMLs comprising nonmagnetic thermoelectric materials,i.e., Bi-Sb and Bi-Sb-Te, has recently been reported37, hybridizing ANE/AEE and its feature superior to ONE/OEE has not been demonstratedand magnetic topological materials have not been incorporated intoAMTLs so far. By means of the thermoelectric imaging techniquebased on lock-in thermography (LIT), we visualize the spatial dis-tribution of transverse thermoelectric charge-to-heat current conver-sion processes in ATMLs based on amagnetic topologicalmaterial andobtain large transverse thermoelectric cooling. Systematic LITexperiments separate the contribution of M-dependent AEE fromM-independent ODPE, confirming theM-induced tuning of transversethermoelectric conversion by hybridizing ANE/AEE in the magnetictopological material. Thermopower measurements reveal that theANE-induced modulation of zT for transverse thermoelectric conver-sion in ATMLs is several times larger than zT for ANE alone in singlemagnetic materials ever reported, owing to the existence of M-inde-pendent ODSE. The development of ATML-based transversemagneto-thermoelectrics will boost research on thermoelectric device applica-tions as well as topological materials science.ResultsFabrication of Co2MnGa-based artificially tilted multilayersAs themagnetic component of ATML, we selected aWeyl ferromagnetCo2MnGa alloy, which is one of themagnetic topologicalmaterials andexhibits not only a top-level transverse thermopower due to ANE (6-8μV/K) owing to its topological feature but also a relatively largenegative Seebeck coefficient SS (around −30 μV/K) among ferromag-netic conductors19,26,38–40. The thermoelectric component of ATMLwaschosen fromaviewpoint of improvingODSE/ODPE inATML.Generally,a combination of two materials with large difference in SS and withsignificantly different electrical and thermal conductivities (σ and κ,respectively) enhances the transverse thermoelectric performance forODSE/ODPE in ATML29–37. Thus, as the thermoelectric component ofCo2MnGa-based ATML, we mainly focused on p-type Bi0.2Sb1.8Te3,which exhibits large positive SS ( > 100 μV/K) andmuch smaller σ and κthan Co2MnGa41.To determine the structure of ATML, we analytically calculatedthe transverse thermoelectric conversion performance of Co2MnGa/Bi0.2Sb1.8Te3 ATML through measuring the electrical, thermal, andthermoelectric transport properties of single Co2MnGa andBi0.2Sb1.8Te3 alloys (see Methods). The transport properties of ourpolycrystalline Co2MnGa and Bi0.2Sb1.8Te3 alloys prepared by sparkplasma sintering (SPS) are summarized in Supplementary Table 1. Theσ and SS values at a magnetic field of 0 T and 0.8 T are almost identicalin Co2MnGa and Bi0.2Sb1.8Te3, indicating that the ordinary/anisotropicmagnetoresistance and magneto-Seebeck effects are negligibly smallin these materials below 0.8T. The κ value of Co2MnGa is much largerthan that of Bi0.2Sb1.8Te3; such a large difference in κmakes it suitablefor constructing ATMLs. Using σ, κ, and SS values of the Co2MnGa andBi0.2Sb1.8Te3 slabs, the electrical and thermal conductivities orthogo-nal to each other (σxx and κyy) and the transverse thermopower due toODSE (SOD) were simulated for Co2MnGa/Bi0.2Sb1.8Te3 ATML, accord-ing to the equations in ref. 36 (see Supplementary Note 1). Figure 2a–drespectively display the contour maps for SOD, σxx, κyy, and zT forsimulated ODSE, zODT (= S2ODσxxT=κyy), in Co2MnGa/Bi0.2Sb1.8Te3ATML as functions of a tile angle θ and thickness ratio R = tM/(tTE + tM)at the zero magnetic field, where tM(TE) is the thickness of magnetic(thermoelectric) layer andT = 300Kwas used. Here, it is found that thevalues of θ ~ 30° and R ~ 0.5 in Co2MnGa/Bi0.2Sb1.8Te3 ATML satisfy theoptimal zODT (~0.13), which is much larger than zT for ANE in single-magnetic materials.Based on the above simulation, Co2MnGa-based ATML was pre-pared by following procedures (see also Methods). Initially, we pre-pared a cylindrical Co2MnGa slab with a diameter of 20mm throughthe SPS method, subsequently slicing it into several disks each with tMof 0.75mm. Then, these sliced Co2MnGa discs and Bi-Sb-Te powderswere alternately piled up and bonded together via SPS. Notably, the Bi-Sb-Te powder used here is identical to that utilized in sintering thesingle Bi0.2Sb1.8Te3 slab. Here, we confirmed that the sharp repeatingFig. 1 | Hybrid transverse magneto-thermoelectric conversion in artificiallytilted multilayers using magnetic topological materials. Schematics of the off-diagonal Seebeck/Peltier effect (ODSE/ODPE) in an artificially tilted multilayer(ATML) comprising magnetic and thermoelectric materials and the anomalousNernst/Ettingshausen effect (ANE/AEE) in the magnetic material. Here, Jc, Jq, andM denote the charge current, heat current, and magnetization, respectively.Article https://doi.org/10.1038/s41467-024-53723-2Nature Communications |         (2024) 15:9643 2www.nature.com/naturecommunicationsboundaries in the Co2MnGa/Bi0.2Sb1.8Te3 stack through structuralcharacterizations; the composition of the bulk regions of eachlayer was uniform and the atomic interdiffusionwas limited to a regionof ~10μm at the Co2MnGa/Bi0.2Sb1.8Te3 interfaces (SupplementaryFig. 1). Finally, the Co2MnGa/Bi0.2Sb1.8Te3 stacks were cut into a rec-tangular slab with a size of ~15 × 2 × 2 mm3 and θ ~ 30°. Throughmicroscopic analysis, we estimated the tTE value of our Co2MnGa/Bi0.2Sb1.8Te3 ATML to be 1.0mm, resulting in the R value of 0.43. Thisconfirms the fabrication of Co2MnGa/Bi0.2Sb1.8Te3 ATML with the θand R values close to the optimal conditions for zODT, as depictedin Fig. 2d.To check the thermoelectric transport property in our poly-crystalline Co2MnGa, we measured ANE using the plain Co2MnGa slab(Supplementary Fig. 2). The anomalous Nernst coefficient of ourCo2MnGa is estimated to be 6.9 μV/K, which is comparable to thevalues in bulk single-crystalline Co2MnGa19,38 as well as polycrystallineCo2MnGa40,42. The σ (κ) value of our polycrystalline Co2MnGa is almostsame as (smaller than) that of single-crystalline Co2MnGa38.Lock-in thermography measurementTo investigate the transverse thermoelectric conversion processes inour ATML, LIT measurements were conducted (see Methods). The LITtechnique based on the infrared thermometry enables the visualiza-tion of the temporal response and spatial distribution of temperaturechanges induced by an external periodic input with high temperature(< 0.1mK) and spatial (around 10–20μm) resolutions43. In LIT mea-surements, heating or cooling signals harmonically oscillating at thefrequency of the periodic input signal are extracted as thermalimages37,44–48. In this study, a square-wave-modulated charge currentwith the frequency f (= 0.2–10.0Hz), amplitude Jc (= 1 A), and zerooffset was applied to the sample along its longitudinal direction (x-axisin Fig. 3a, i), which induces temperature changes due to the thermo-electric conversion as well as Joule heating. By extracting the firstharmonic component of the thermal images, the contribution of thethermoelectric effects (∝ Jc) can be retrieved free from that of Jouleheating (∝ Jc2)46,47. The captured thermal images were transformed intolock-in amplitude A and phase ϕ images through Fourier analysis,where the A (ϕ) image shows the distribution of the magnitude (sign)of the induced temperature modulation and the ϕ image also givesinformation on the time delay of the temperature modulation due tothermal diffusion. We carried out the LIT measurements in two con-figurations: cross-section (Fig. 3a) and top-side configurations (Fig. 3i).Visualization of off-diagonal Peltier effect in Co2MnGa-basedartificially tilted multilayerFigure 3 shows the results of the LIT measurements for Co2MnGa/Bi0.2Sb1.8Te3 ATML in the absence of H. First, we examine the resultsfor the cross-section configuration (Fig. 3a–h). The A and ϕ images atf = 10.0Hz (top panels) and 0.2Hz (bottom panels) are displayed inFig. 3c, d, respectively. We can obtain information on the transient(nearly steady-state) temperature distribution induced by thermo-electric effects at f = 10.0Hz (0.2 Hz)37,46. At f = 10.0Hz, temperaturemodulation signals are obtained in the vicinity of the interfacesbetween the Co2MnGa and Bi0.2Sb1.8Te3 layers; the A value reaches amaximum at the oblique junction interfaces and the 180° reversal ofϕbetween the neighboring interfaces appears due to the Peltier effect.Importantly, in contrast to a Peltier-effect-induced temperature mod-ulation at non-oblique junction interfaces49,50, the A signal is non-uniform along the oblique interfaces owing to the non-uniform Jc flowin ATML, which is the origin of the transverse thermoelectric conver-sion stemming from ODPE. At f =0.2Hz, the cooling/heating signalsare broadened through thermal diffusion, and the A and ϕ signalsexhibit zigzag-shaped patterns with an angle corresponding to a θvalue of ~30°. As shown in the bottom panel of Fig. 3d, the ϕ value atthe upper (lower) edge of the sample presents almost uniform valuesof ~180° ( ~0°) (see also the x-directional line profile shown in Fig. 3f),confirming transverse thermoelectric cooling and heating due toODPE in Co2MnGa/Bi0.2Sb1.8Te3 ATML. Note that the A value periodi-cally changes along the x direction because of the multilayer structure(Fig. 3e). The transverse thermoelectric cooling behavior canbe clearlyidentified in the top-side configuration (Fig. 3i–n).To evaluate the transverse thermoelectric cooling/heating per-formance of Co2MnGa/Bi0.2Sb1.8Te3 ATML, we averaged the LIT resultsover one Co2MnGa/Bi0.2Sb1.8Te3 unit. Figure 3g,h (3o,p) shows the fdependence of the averaged A and ϕ values, Aave and ϕave, for oneCo2MnGa/Bi0.2Sb1.8Te3 unit in the cross-section (top-side) configura-tion, where the averaged areas are defined in Fig. 3c,d (3k,l). In bothconfigurations, the Aave value monotonically increases and the ϕaveFig. 2 | Simulation of transverse thermopower and electrical/thermal con-ductivity for Co2MnGa/Bi0.2Sb1.8Te3 ATML. a–d Contour maps depicting thetransverse thermopower due to ODSE SOD (a), electrical conductivity along the Jcdirection σxx (b), thermal conductivity along the Jq direction κyy (c), and dimen-sionless figure of merit for ODSE zODT (= S2ODσxxT=κyy) at zero magnetic field andthe temperature T = 300K (d) as functions of the tilt angle of ATML θ and thicknessratio R defined as R = tM/(tM+ tTE) with tM(TE) being the thickness of the magnetic(thermoelectric) layer.Theopendiamond symbol in (d) represents theθ (=30° ± 1°)and R (= 0.43) values for our sample. θ was estimated from the thermal imagesobtained for lock-in thermography (LIT).Article https://doi.org/10.1038/s41467-024-53723-2Nature Communications |         (2024) 15:9643 3www.nature.com/naturecommunicationsvalue gradually gets closer to 180° with decreasing f, that is,approaching the temperature distribution in the steady state. Theobserved transverse thermoelectric temperature modulation is ~1 K atf =0.2Hz, which is much larger than that generated only by using OEEor AEE in a single conductor in a similar experimental condution11,12,51.Transverse magneto-thermoelectric conversion in Co2MnGa-based artificially tilted multilayerNext, we investigate the temperature modulation induced by trans-verse magneto-thermoelectric effects in Co2MnGa/Bi0.2Sb1.8Te3 ATMLfrom the LIT images captured under an application of H with themagnitude of H. To hybridize ODPE and AEE, H was applied along thevertical direction (z axis in Fig. 3a) [horizontal short direction (y axis inFig. 3i)] of the sample in the cross-section (top-side) configurationusing electromagnets. The temperature change arising from thetransverse magneto-thermoelectric effects, namely, AEE and/or OEE,exhibits an antisymmetric dependencewith respect to theH direction,whereas the temperature change due to ODPE and/or the ordinary/anisotropic magneto-Peltier effect showcases a symmetric depen-dence (note again that the contribution of the ordinary/anisotropicmagneto-Peltier effect, the Onsager reciprocal of the ordinary/aniso-tropic magneto-Seebeck effect, is negligible in our samples). Thus, wecalculate H-odd-dependent LIT signals using the following equations:Aodd = A +Hð Þe�iϕ +Hð Þ � A �Hð Þe�iϕ �Hð Þ�� ��=2 ð1Þϕodd = � arg A +Hð Þe�iϕ +Hð Þ � A �Hð Þe�iϕ �Hð Þ� � ð2Þwhere A(+H) [ϕ(+H)] and A(−H) [ϕ(−H)] are defined as A (ϕ) measuredin the positive (−z or +y direction) and negative (+z or −y direction) H,respectively. Figure 4a, b shows the Aodd and ϕodd images forCo2MnGa/Bi0.2Sb1.8Te3 ATML at μ0|H| = 0.8 T and f = 10.0Hz (toppanels) and 0.2Hz (bottom panels) in the cross-section configuration,where μ0 represents the vacuum permeability. The distribution of theAodd and ϕodd signals inside ATML is obviously different from thatarising from ODPE at zero magnetic field (Fig. 3c, d). As highlighted inthe images at f = 10.0Hz, the Aodd and ϕodd signals appear in theCo2MnGa regions. Importantly, despite their different distributions,the H-odd-dependent components contribute to the transversethermoelectric cooling/heating with the same symmetry as ODPE(compare the thermal images at f = 0.2Hz in Figs. 3d and 4b).Hereafter, we focus on the results for the top-side configurationbecause the signals at the sample edges in the cross-sectionFig. 3 | Transverse thermoelectric conversion in Co2MnGa/Bi0.2Sb1.8Te3 ATMLat zero magnetic field. a Schematic of the sample structure in the cross-sectionconfiguration. b Steady-state temperature image during the LITmeasurement in thecross-sectionconfiguration.c,dLock-inamplitudeA (c) andphaseϕ (d) imagesat thelock-in frequency f= 10.0and0.2Hz.e, fx-directionalA (e) andϕ (f) profiles along thewhite dotted lines in the top panels of c and d, respectively. g, h f dependence of theaveraged lock-in amplitude Aave (g) and phase ϕave (h) values over one Co2MnGa/Bi0.2Sb1.8Te3 unit. i–p Results for the top-side configuration. The Aave andϕave valuesin g and h (o andp) were estimated by averaging A andϕ signals in the areas definedby thewhite rectangles in c and d (k and l), corresponding to the blue shaded area ineand f (mandn), respectively. In all theLITmeasurements, a square-wave-modulatedcharge current with an amplitude of 1 A and zero offset was applied.Article https://doi.org/10.1038/s41467-024-53723-2Nature Communications |         (2024) 15:9643 4www.nature.com/naturecommunicationsconfiguration are difficult touse for quantitative discussions due to thelimitation of spatial resolution of LIT37. Figure 5a, b shows the Aodd andϕodd images for Co2MnGa/Bi0.2Sb1.8Te3 ATML at μ0|H| = 0.8 T andf = 10.0Hz and 0.2Hz in the top-side configuration. At f = 10.0Hz, theAodd signals in the Co2MnGa regions are greater than those in theBi0.2Sb1.8Te3 regions and the ϕodd signals are reversed between theCo2MnGa (~0°) and Bi0.2Sb1.8Te3 (~180°) regions. As shown in Fig. 5c, d,in the μ0|H| range of 0.2–1.0 T, the Aodd value is almost constant in theCo2MnGa region with ϕodd ~ 0°, while the Aodd value linearly increaseswith increasing H in the Bi0.2Sb1.8Te3 region with ϕodd ~ 180°. Thesetendencies are consistent with the H dependence of the ANE signal inCo2MnGa and that of the ONE signal in Bi0.2Sb1.8Te3 (SupplementaryFig. 2), indicating that the A and ϕ images measured at non-zero Hcontain the contributions of AEE in Co2MnGa as well as OEE inBi0.2Sb1.8Te3. At lower f, the LIT images exhibit different temperaturedistributions as a result of superimposed contributions of AEE andOEEthrough thermal diffusion; the almost uniformϕodd signal (~0°) acrossthe entire sample area is observed at f =0.2Hz with the enhanced Aoddsignal. Figure 5e, f shows the f dependence of the Aodd and ϕodd valuesin theCo2MnGa andBi0.2Sb1.8Te3 regions, respectively.With approach-ing the steady state, theAodd valuemonotonically increases in both theCo2MnGa and Bi0.2Sb1.8Te3 regions (Fig. 5e), while the ϕodd valueremains ~0° in the Co2MnGa region and gradually changes from ~180°to ~0° in theBi0.2Sb1.8Te3 region (Fig. 5f). These results indicate that theAEE-induced Jq from the Co2MnGa layer predominantly affects thetemperature change even on the Bi0.2Sb1.8Te3 surface, suggesting thatANE/AEE in Co2MnGa modulates the transverse thermoelectricconversion in Co2MnGa/Bi0.2Sb1.8Te3 ATML in the steady state.To verify our interpretation that the Aodd and ϕodd signals stemfrom ANE in Co2MnGa, we must distinguish the ANE contribution fromthe Seebeck-effect-driven anomalous Hall effect (AHE) observed inmagnetic/thermoelectric hybrid systems40,52,53, which can superimposeadditional transverse thermopower onto ANE via the combination ofthe Seebeck effect in thermoelectric layers and AHE in magnetic layers.To this end, we performed the same LIT measurements for Co2MnGa/Bi2Te3 ATML, in which p-type Bi0.2Sb1.8Te3 was replaced by n-typeBi2Te3. Here, the sign of the contribution of Seebeck-effect-driven AHEshould be reversed due to the different sign of SS between Bi0.2Sb1.8Te3and Bi2Te3. The fabrication procedure of ATML and the optimizationconditions of ODSE for Co2MnGa/Bi2Te3 ATML are the same as thosefor Co2MnGa/Bi0.2Sb1.8Te3 ATML (Methods and Supplementary Fig. 3).The results of the LIT measurements for Co2MnGa/Bi2Te3 ATML aresummarized in Supplementary Figs. 4–6. The direction of ODPE-induced Jq is opposite and the magnitude of temperature modulationdecreases, compared with that of Co2MnGa/Bi0.2Sb1.8Te3 ATML. This isbecause the sign (magnitude) of the difference in the Peltier coefficient( = SST) between the magnetic and thermoelectric components ofATMLs, ΔSST with ΔSS being the difference in SS, was reversed(reduced) by changing the sign of SS of the thermoelectric componentfrom positive to negative. On the other hand, the H-odd component ofthe LIT signals in Co2MnGa/Bi2Te3 ATML is comparable to that inCo2MnGa/Bi0.2Sb1.8Te3 ATMLbecause of almost identical thermopowerdue to ONE between Bi0.2Sb1.8Te3 and Bi2Te3 (Supplementary Table 1and Supplementary Fig. 2). Since the sign of the transverse thermo-power due to ANE in Co2MnGa and Seebeck-effect-driven AHE inbilayers consisting of Co2MnGa and n-type (p-type) thermoelectricmaterials is the same (opposite)53,54, the transverse magneto-thermoelectric conversion in Co2MnGa/Bi2Te3 ATML should beimproved over that in Co2MnGa/Bi0.2Sb1.8Te3 ATML if Seebeck-effect-driven AHE contributes effectively to ATMLs. However, the observedAodd value in the Co2MnGa region of Co2MnGa/Bi2Te3 ATML is slightlysmaller than that of Co2MnGa/Bi0.2Sb1.8Te3 ATML, which could beexplained by electrical shunting in Bi0.2Sb1.8Te3 and Bi2Te3. Theseresults indicate that the contribution of Seebeck-effect-driven AHE onthe total transverse magneto-thermopower is much smaller than thatof ANE in our samples due to the unoptimized θ value and size ratio ofthemagnetic and thermoelectric layers for themagneto-thermoelectriceffects (note that θ in our samples is designed for ODSE).Hybrid transverse magneto-thermoelectric conversionHere, we discuss the ANE-induced modulation of the total transversethermoelectric conversion in our Co2MnGa-based ATMLs. From anapplication viewpoint, the performance of the temperature modula-tion in the steady state is important; therefore, we focused on theresults at the minimum f (= 0.2 Hz). Figure 6a, b displays the Hdependence of the Aave and ϕave signals at f =0.2Hz for Co2MnGa/Bi0.2Sb1.8Te3 and Co2MnGa/Bi2Te3 ATMLs in the top-sideFig. 5 | Contributionof transversemagneto-thermoelectric effects inCo2MnGa/Bi0.2Sb1.8Te3 ATML in top-side configuration. a, b Aodd (a) andϕodd (b) images atμ0|H| = 0.8 T and f = 10.0 and 0.2Hz in Co2MnGa/Bi0.2Sb1.8Te3 ATML. Here, H wasapplied along the horizontal short direction of the sample (y axis in Fig. 3i). c, d |H|dependence of Aodd (c) and ϕodd (d) at f = 10.0Hz. Solid lines in c represent theresults of linear fitting. e, f f dependenceofAodd (e) andϕodd (f) atμ0|H| = 0.8 T. Thedata points in c–fwere obtainedby averaging the temperaturemodulation signal inthe area definedby the greenandorange rectangles ina andb for theCo2MnGaandBi0.2Sb1.8Te3 areas, respectively.Fig. 4 | Contribution of transverse magneto-thermoelectric effects inCo2MnGa/Bi0.2Sb1.8Te3 ATML in cross-section configuration. a, b H-odd-dependent component of the lock-in amplitude Aodd (a) and phaseϕodd (b) imagesat μ0|H| = 0.8 T and f = 10.0 and 0.2Hz in Co2MnGa/Bi0.2Sb1.8Te3 ATML. Here, themagnetic field H with the magnitude of H was applied along the vertical direction(z axis in Fig. 3a) of the sample and μ0 is the vacuum permeability.Article https://doi.org/10.1038/s41467-024-53723-2Nature Communications |         (2024) 15:9643 5www.nature.com/naturecommunicationsconfiguration. In both ATMLs, the magnitude of Aave exhibits the clearasymmetric H dependence with a saturation behavior, which is con-sistent with the magnetization curve of Co2MnGa in ATMLs (displayedin Fig. 6a, b), owing to the AEE contribution. Because of the dominantODPE contribution and the positive (negative) ΔSS for Co2MnGa/Bi0.2Sb1.8Te3 (Co2MnGa/Bi2Te3) ATML, anH-independent ϕave value of~180° (~0°) appears in Co2MnGa/Bi0.2Sb1.8Te3 (Co2MnGa/Bi2Te3)ATML. TheAave value is enhanced by applying the negative (positive)Hin Co2MnGa/Bi0.2Sb1.8Te3 (Co2MnGa/Bi2Te3) ATML because the direc-tion of generated Jq due to ODPE at zeroH is opposite to (the same as)that due to AEE at the positive H. The H-induced modulation ratio ofthe temperature change for Co2MnGa/Bi0.2Sb1.8Te3 and Co2MnGa/Bi2Te3 ATMLs is estimated to be |Aave(+H) −Aave(−H)|/Aave(0T) ~ 5% and15% at μ0|H| > 0.2 T, respectively. The larger H-induced modulationratio for Co2MnGa/Bi2Te3 ATML is due to the smaller ODPE contribu-tion [=Aave(0 T)]. These results reveal that AEE can exert a clear changein the average temperature modulation in ATMLs, although AEEappears only in the Co2MnGa layers.To quantitatively evaluate the thermoelectric performance basedon the hybrid action of ODSE and ANE, we measured the transversethermopower by applying a temperature difference ΔT between thetop and bottom surfaces of Co2MnGa-based AMTLs (see also Meth-ods). Figure 7a, b shows the H dependence of the transverse thermo-electric voltage VT at various values of ΔT for Co2MnGa/Bi0.2Sb1.8Te3and Co2MnGa/Bi2Te3 ATMLs, respectively. With increasing ΔT, boththe offset thermoelectric voltage due to ODSE and the H-inducedchange in the thermoelectric voltage due to ANE increase. Here,only the sign of the ODSE contribution is reversed between Co2MnGa/Bi0.2Sb1.8Te3 and Co2MnGa/Bi2Te3 ATMLs because of the signreversal of ΔSS. Figure 7c shows the temperature gradient ∇T depen-dence of the transverse thermoelectric field ET at μ0H = ±0.8 T. Theapplication of H clearly changes the slope of the ET-∇T plots, i.e., thetransverse thermopower ST; the negative (positive) H applicationenhances the magnitude of ST of Co2MnGa/Bi0.2Sb1.8Te3 (Co2MnGa/Bi2Te3) ATML.By combining the measured ST values and simulated σxx and κyyvalues (Fig. 2b, c and caption in Fig. 7), we estimate the figure of meritfor hybrid transverse magneto-thermoelectric conversion zTT(= S2TσxxT=κyy) atT = 300K to be0.088 and0.095 (0.010 and0.008) at+0.8 and −0.8 T, respectively, for Co2MnGa/Bi0.2Sb1.8Te3 (Co2MnGa/Bi2Te3) ATML. These zTT values are several orders of magnitude largerthan zT for ANE, zNT, in singlemagnetic materials ( < 7 × 10−4 at 300K).Most importantly, in our Co2MnGa-basedATMLs, especiallyCo2MnGa/Bi0.2Sb1.8Te3 ATML, the M-dependent change in zTT is also severaltimes larger than zNT. The reason why we achieve such a significanttransverse magneto-thermoelectric modulation, surpassing therecord-high zNT, is owing to the presence of M-independent ODSE.Since the zT value is proportional to the square of the thermopower,Fig. 6 | Hybrid transversemagneto-thermoelectric temperaturemodulation inCo2MnGa-based ATML. H dependence of the averaged Aave and ϕave signals atf =0.2Hz for Co2MnGa/Bi0.2Sb1.8Te3 (a) and Co2MnGa/Bi2Te3 (b) ATMLs. Themagnetization M curves of Co2MnGa in each ATML measured using a vibratingsample magnetometer are also shown (note that Bi0.2Sb1.8Te3 and Bi2Te3 arenonmagnetic).Fig. 7 | Hybrid transverse magneto-thermoelectric generation in Co2MnGa-based ATML. a, b H dependence of the transverse thermoelectric voltage VT atvarious ΔT values for Co2MnGa/Bi0.2Sb1.8Te3 (a) and Co2MnGa/Bi2Te3 (b) ATMLs.ΔT denotes the temperature difference between the top and bottom surfaces ofATML. c ∇T dependence of the transverse electric field ET ( =VT/l) for Co2MnGa/Bi0.2Sb1.8Te3 and Co2MnGa/Bi2Te3 ATMLs at μ0H = ±0.8 T. ∇T and l denote tem-perature gradient and sample length, respectively. The transverse thermopowerST, estimated by linear fitting, is −55.2 (+18.3) μV/K at +0.8 T and −57.1 (+16.2) μV/Kat −0.8 T for Co2MnGa/Bi0.2Sb1.8Te3 (Co2MnGa/Bi2Te3) ATML. The inset shows aschematic of the set-up for measuring the transverse thermopower.Article https://doi.org/10.1038/s41467-024-53723-2Nature Communications |         (2024) 15:9643 6www.nature.com/naturecommunicationszNT and zTT satisfy the following relations:zNT / S2N ð3ÞzTT / S2T = SOD +eSN� �2= S2OD + 2SODeSN +eS2N ð4Þwhere eSN is the effective anomalous Nernst coefficient considering thereduction due to the superimposition of ONE and the shunting effectin ATMLs. In ATMLs, the ANE contribution for zTT produces theadditional 2SODeSN term of which magnitude depends on both SN andSOD (i.e., ST at μ0H =0T), resulting that the magneto-thermoelectricmodulation of zTT gets much greater than zNT owing to larger |SOD|than |SN| . In fact, such a hybridization of ODSE and ANE is moreprominent in Co2MnGa/Bi0.2Sb1.8Te3 ATML (SOD = −56.1 μV/K) than inCo2MnGa/Bi2Te3 ATMLs (SOD = +17.2 μV/K). Thus, this unconventionalsynergy offers another route to develop physics and materials scienceon ANE.DiscussionFinally, we discuss prospects for advancing the ANE-hybridizedtransverse magneto-thermoelectric conversion in ATMLs. Exploring amagnetic material showing large SN, which is the current mainstreamresearch in spin caloritronics and topological materials science, isproperly significant. If one can develop a material that exhibits twicelarger SN than Co2MnGa, for example, by introducing it in place ofCo2MnGa in Co2MnGa/Bi0.2Sb1.8Te3 ATML, the ANE-induced modula-tion of zTT reaches 0.01 at room temperature. In addition to ANE, thelarge magnitude of the base transverse thermopower at zero field duetoODSE is also indispensable, according to the results shown in the lastsection; a superior ODSE performance, e.g., larger ΔSS in ATMLs, canenhance the magneto-thermoelectric modulation even if the con-tribution of ANE alone is the same. Supplementary Fig. 7a shows thedependence of the absolute value of eSN on the magneto-thermoelectric modulation of zTT, i.e., Δ(zTT) = eS2N + 2��SODeSN��, at var-ious magnitudes of SOD. The presence of ODSE not only significantlyimproves the Δ(zTT) value without changing��eSN�� but also furtherincreases the contribution of ANE on Δ(zTT), i.e., the slope in Supple-mentary Fig. 7a, resulting in Δ(zTT) ~ 0.05 (~0.13) at��eSN�� = 7 μV/K (20μV/K) and SOD�� �� = 100 μV/K at room temperature (note that over 100μV/K of SOD�� �� has been reported in many ATMLs in previousstudies32–35,37). Furthermore, as shown in Supplementary Fig. 7b,improving botheSN and SOD canenhance the zTT value, e.g., zTT ~ 0.35 at��eSN�� = 7 μV/K and��SOD�� = 100 μV/K at room temperature. These find-ings emphasize the importance of investigating both ANE and ODSE(i.e., SN and SS), whichhave been studied independently. Especially, theexploration of magnetic materials with large SS has received littleattention so far, leading to new research on magnetic materials.Interface engineering in ATMLs is also promising since multilayeringcould increase SN itself intentionally via an interfacial spin-orbitinteraction55. Further superimposition of the contribution ofmagneto-thermoelectric effects other than ANE is another route for improvingthe performance of transverse thermoelectric conversion in ATMLs.Since this study focuses on the demonstration of hybridizing ANE inATMLs using amagnetic topological material, the contribution of ONEwas not optimized; the opposite sign of SN in Bi0.2Sb1.8Te3 or Bi2Te3against SN in Co2MnGa decreases the magneto-thermoelectric mod-ulation. Optimizing the θ value and size ratio of magnetic and ther-moelectric layers is also effective for further manifesting thecontribution of Seebeck-effect-driven AHE in ATMLs. By appropriatelydesigning these factors and includingODSE, ANE,ONE, Seebeck-effect-driven AHE, and other magneto-thermoelectric effects, dramaticimprovements in the transverse magneto-thermoelectric conversionperformance are possible in ATMLs.In summary, we have demonstrated the giant ANE-induced mod-ulation of transverse thermoelectric conversion that far exceeds theperformance of ANE alone by fabricating ATMLs using a Weyl ferro-magnet Co2MnGa and thermoelectric materials. The infrared imagingtechnique based on LIT visualized the current-induced transversethermoelectric cooling/heating behaviors. The LIT measurementsunder variousH values clarified the contributions of structure-inducedODPE, H-induced OEE, andM-induced AEE in Co2MnGa-based ATMLs,proving the modulation of the transverse thermoelectric conversionperformance due to hybridization of ODSE and ANE in Co2MnGa.Owing to the existence of ODSE, the magneto-thermoelectric mod-ulation of zTT in Co2MnGa-based ATMLs induced by ANE was muchgreater than zNT in a single Co2MnGa alloy that exhibits the record-high ANE performance at room temperature. The hybrid transversemagneto-thermoelectric conversion in ATMLs is potentially availableeven in the absenceofmagnetic fields; by utilizing permanentmagnetswith finite remanent magnetization as a magnetic component ofATML37,56, not only ANE in the ferromagnetic layers but also ONE in thethermoelectric layers can be superimposed without external magneticfields57, eliminating the unnecessary electricity for magnetic fieldapplications. The interdisciplinary fusion of transverse thermo-electrics by ANE and ODSE in ATMLs will stimulate research on ther-moelectric applications in the topological materials sciencecommunity more actively and open new directions for thermoelectricmaterial exploration.MethodsPreparation of Co2MnGa, Bi0.2Sb1.8Te3, and Bi2Te3 slabs andCo2MnGa-based ATMLTo prepare Co2MnGa ingots, 99.97% purity Co, 99.99% purity Mn, and99.9999% purity Ga shots (RARE METALLIC Co., Ltd.) were arc-meltedwith an atomic ratio of 2:1:1 in an Ar atmosphere. The resulting arc-melted ingot was homogenized in high vacuum at 1000 °C for48 hours, followedby600 °C for 72 hours. Subsequently, the ingotwascrushed using planetary ball mill and sieved through a 100-μm mesh.TheCo2MnGapowderwas subsequently sintered into a cylindrical slabwith a diameter of 20mm at 850 °C and a pressure of 30MPa for60minutes in a vacuum chamber by the SPS method. Bi0.2Sb1.8Te3(Bi2Te3) ingots with a diameter of 20mm and a height of 15mm wereprepared from 99.9% purity Bi-Sb-Te (Bi2Te3) powders, available fromToshima Manufacturing Co., Ltd, via the SPS method at 450 °C and30MPa for 60minutes under the vacuum condition. The compositionratio of sintered Bi-Sb-Te slabs was confirmed to be Bi0.2Sb1.8Te3 usingscanning electron microscopy (SEM) with energy-dispersive X-rayspectroscopy (EDS) (Cross-Beam 1540ESB, Carl Zeiss AG). The poly-crystalline nature of Co2MnGa, Bi0.2Sb1.8Te3, and Bi2Te3 alloys pre-pared by the above procedures were also obtained by SEM-EDS. Forcharacterization of transport properties, the Co2MnGa (Bi0.2Sb1.8Te3andBi2Te3) ingotwas cut into a rectangular slabwith a size of ~10 × 1 × 1mm3 (~12 × 3 × 1 mm3) using a diamond wire saw. Here, for theBi0.2Sb1.8Te3 and Bi2Te3 slabs, two rectangular slabs with differentcutout directions were prepared (see Supplementary Note 2and Fig. 8).To fabricate Co2MnGa-based ATMLs, the prepared cylindricalCo2MnGa slab was sliced into many disks using the diamond wire saw.The SPS sintering for the Co2MnGa/Bi0.2Sb1.8Te3 and Co2MnGa/Bi2Te3stacks was carried out at 450 °C and 30MPa for 60minutes in thevacuum chamber. The elemental distribution of the stacks was char-acterized by SEM-EDS (Supplementary Fig. 1). Finally, the preparedCo2MnGa/Bi0.2Sb1.8Te3 and Co2MnGa/Bi2Te3 stacks were cut into arectangular slab of ATML with the diamond wire saw.Measurements of transport properties of single slabThe σ and SS values and their H dependence of single Co2MnGa,Bi0.2Sb1.8Te3, and Bi2Te3 slabs weremeasured using the system similarArticle https://doi.org/10.1038/s41467-024-53723-2Nature Communications |         (2024) 15:9643 7www.nature.com/naturecommunicationsto the Seebeck Coefficient/Electric Resistance Measurement System(ZEM-3, ADVANCE RIKO, Inc.)58,59. Here, the sample was clampedbetween two Cu blocks whose temperatures were independentlycontrolled using ceramic heaters and Pt100 temperature sensors. Hwas applied along the short axis of the samples using an electro-magnet. R-type (PtRh-Pt) thermocouple probes were attached to thesample to simultaneously measure the electric voltage and tempera-ture difference. Simultaneous measurements of the generated ther-moelectric voltage and temperature difference between the twothermocouple probes in the direction parallel to the applied ∇Tthrough the Cu blocks enables accurate estimation of SS. The SS valuewas quantified by fitting the temperature difference dependence ofthe thermoelectric voltage to a linear function. Themagnitude of σwasevaluated via the standard four-terminal method by applying a chargecurrent through the Cu blocks. The κ value was evaluated by multi-plying the thermal diffusivity measured using the laser flash method,the specific heat using the differential scanning calorimetry, and thedensity using the Archimedes method. SN was measured using ahomemade temperature gradient generator combined with an elec-tromagnet through a method similar to that described in ref. 52 (seealso Supplementary Fig. 3). The sample was bridged onto two surface-anodized Al blocks, where one of the Al blockswas thermallymountedon a heat bath and the other had a chip heater to apply∇T. The surfaceof the sample was coated with black ink and the magnitude of ∇T wasmeasured with the infrared camera. While sweepingH in the directionperpendicular to ∇T, generated VT in the direction perpendicular toboth∇T andHwasmeasured. The SN valuewas estimated byfitting the∇T dependence of ET, i.e., VT divided by the sample width, with a linearfunction (Supplementary Fig. 3). All measurements were performed atroom temperature and atmospheric pressure.LIT measurementsThe LIT measurements were conducted with Enhanced Lock-In Ther-mal Emission (ELITE, DCG Systems G.K.) at room temperature andatmospheric pressure. For the LITmeasurements under the verticalH,the ATML samples were directly mounted on the center of an elec-tromagnet to ensure the uniform H. For the LIT measurements underthe horizontal H, the ATML samples were securely mounted on aphenolic resin plate with low thermal conductivity to minimize theheat leakage through thermal conduction. To improve infrared emis-sivity and ensure uniform emission properties during the LIT mea-surements, the top and side surfaces of the samples were coated withinsulating black ink whose emissivity is > 0.94 (JSC-3, JAPANSENSORCorporation). The minimum f value during the LIT measurements wasdetermined by considering the thermal boundary conditions; wechose 0.2Hz as a minimum f because we have confirmed that there isno influence of parasitic signals, such as the Peltier effect at the sampleedges due to wiring, to the signal on the sample in the viewing area ofLIT at 0.2 Hz. The viewing area of all the lock-in images is 512 × 260pixels = 7.68 × 3.90 mm2.Measurements of transverse thermopower in Co2MnGa-based ATMLsA schematic of the measurement set-up for the transverse thermo-power in Co2MnGa-based ATMLs is shown in the inset of Fig. 7c. TheATML samples for thermopower measurements were fixed on a heatbathmade of a surface-anodized Al block. To apply ∇T to the samples,a chip heater was attached to the top surface of the sample and asapphire substrate was inserted between the heater and sample toensure uniform temperature gradient application. The ∇T value wasdetermined using the infrared camera by coating the side surface ofthe samplewith theblack ink. During sweepingH in thewidthdirectionof the samples perpendicular to ∇T, VT in the longitudinal directionwasmeasured. 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This workwas partially supported by ERATO “Magnetic Thermal ManagementMaterials Project” (No. JPMJER2201) from JST, Japan; Grant-in-Aid forScientific Research (S) (No. 22H04965) from JSPS KAKENHI, Japan; andNEC Corporation (K.U.).Author contributionsT.H. and K.U. planned and designed the experiments, prepared thesamples, and performed the LIT experiments. T.H. analyzed the LIT data,measured the thermoelectric, electric, thermal transport properties ofthe samples, anddeveloped the explanation of the experimental results.K.U. collectedmagnetic properties of ATMLs. F.A. analytically simulatedthe transport properties in ATMLs. H.S.A conducted the microstructuralcharacterization. T.H. andK.U.wrote themanuscript. K.U. supervised theproject. All authors discussed the results and commented on themanuscript.Competing interestsThe authors declare no competing interests.Article https://doi.org/10.1038/s41467-024-53723-2Nature Communications |         (2024) 15:9643 9https://arxiv.org/abs/2402.18019https://arxiv.org/abs/2402.18019www.nature.com/naturecommunicationsAdditional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-53723-2.Correspondence and requests for materials should be addressed toTakamasa Hirai or Ken-ichi Uchida.Peer review information Nature Communications thanks ChenguangFu, Yumeng Yang and the other anonymous reviewer(s) for their con-tribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-53723-2Nature Communications |         (2024) 15:9643 10https://doi.org/10.1038/s41467-024-53723-2http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications Hybridizing anomalous Nernst effect in artificially tilted multilayer based on magnetic topological material Results Fabrication of Co2MnGa-based artificially tilted multilayers Lock-in thermography measurement Visualization of off-diagonal Peltier effect in Co2MnGa-based artificially tilted multilayer Transverse magneto-thermoelectric conversion in Co2MnGa-based artificially tilted multilayer Hybrid transverse magneto-thermoelectric conversion Discussion Methods Preparation of Co2MnGa, Bi0.2Sb1.8Te3, and Bi2Te3 slabs and Co2MnGa-based ATML Measurements of transport properties of single slab LIT measurements Measurements of transverse thermopower in Co2MnGa-based ATMLs Data availability References Acknowledgements Author contributions Competing interests Additional information