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[Weinan Zhou](https://orcid.org/0000-0003-2946-9913), [Taisuke Sasaki](https://orcid.org/0000-0002-5952-7638), [Ken‐ichi Uchida](https://orcid.org/0000-0001-7680-3051), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550)

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[Direct‐Contact Seebeck‐Driven Transverse Magneto‐Thermoelectric Generation in Magnetic/Thermoelectric Bilayers](https://mdr.nims.go.jp/datasets/00acb3b8-fe74-471a-bb26-fff052dfd7f0)

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Direct‐Contact Seebeck‐Driven Transverse Magneto‐Thermoelectric Generation in Magnetic/Thermoelectric BilayersRESEARCH ARTICLEwww.advancedscience.comDirect-Contact Seebeck-Driven TransverseMagneto-Thermoelectric Generation inMagnetic/Thermoelectric BilayersWeinan Zhou,* Taisuke Sasaki, Ken-ichi Uchida, and Yuya SakurabaTransverse thermoelectric generation converts temperature gradient in onedirection into an electric field perpendicular to that direction and is expectedto be a promising alternative in creating simple-structured thermoelectricmodules that can avoid the challenging problems facing traditionalSeebeck-effect-based modules. Recently, large transverse thermopower hasbeen observed in closed circuits consisting of magnetic and thermoelectricmaterials, called the Seebeck-driven transverse magneto-thermoelectricgeneration (STTG). However, the closed-circuit structure complicates itsbroad applications. Here, STTG is realized in the simplest way to combinemagnetic and thermoelectric materials, namely, by stacking a magnetic layerand a thermoelectric layer together to form a bilayer. The transversethermopower is predicted to vary with changing layer thicknesses and peaksat a much larger value under an optimal thickness ratio. This behavior isverified in the experiment, through a series of samples prepared by depositingFe–Ga alloy thin films of various thicknesses onto n-type Si substrates. Themeasured transverse thermopower reaches 15.2 ± 0.4 μV K−1, which is afivefold increase from that of Fe–Ga alloy and much larger than the currentroom temperature record observed in Weyl semimetal Co2MnGa. The findingshighlight the potential of combining magnetic and thermoelectric materialsfor transverse thermoelectric applications.1. IntroductionWaste heat generated during various industrial and commercialprocesses is an enormous yet mostly untapped energy source,W. ZhouInternational Center for Young ScientistsNational Institute for Materials ScienceTsukuba 305-0047, JapanE-mail: zhou.weinan@nims.go.jpT. Sasaki, K.-ichi Uchida, Y. SakurabaResearch Center for Magnetic and Spintronic MaterialsNational Institute for Materials ScienceTsukuba 305-0047, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/advs.202308543© 2024 The Authors. Advanced Science published by Wiley-VCH GmbH.This is an open access article under the terms of the Creative CommonsAttribution License, which permits use, distribution and reproduction inany medium, provided the original work is properly cited.DOI: 10.1002/advs.202308543and converting it to usable electricity is acrucial component for achieving sustain-able global development. The Seebeck effect(SE), which refers to the generation of anelectric field parallel to the applied temper-ature gradient (∇T), has long been studiedto realize this thermoelectric conversion.[1,2]In the recent decade, transverse thermo-electric generation (TTG), with a well-known example of the anomalous Nernsteffect (ANE) observed in magnetic mate-rials, has been attracting increasing inter-est as an alternative way for such thermo-electric conversion.[3–20] For ANE, an elec-tric field (E) is generated with its directionperpendicular to both ∇T and the magne-tization (M) of the material. The key hereis the orthogonal relationship between Eand ∇T, which allows the ANE-based ther-moelectric modules to have a simple two-dimensional structure made of connectingwires on a surface, in contrast to a compli-cated 3D structure adopted by the SE-basedmodules consisting of alternately placed p-type and n-type semiconductor pillars. Thissimple structure grants better flexibility andscalability to the ANE-based modules, andcould avoid the efficiency losses and thermal degradation thatoccurred at the numerous electrical contacts of the SE-basedmodules.[11,14,16–18,20] These advantages have also been exploitedfor other applications, such as flexible heat flux sensors with lowthermal resistance.[21–24] However, the transverse thermopowerfor ANE is still small compared to the thermopower of SE ofthermoelectric materials, and further enhancement is stronglyrequired for creating practical applications.The thermopower of ANE, anomalous Nernst coefficient SANE,is expressed asSANE = 𝜌xx𝛼xy − SSE𝜌AHE𝜌xx(1)where 𝜌xx, 𝛼xy, SSE, and 𝜌AHE are the longitudinal resistivity,anomalous Nernst conductivity, thermopower of SE (i.e., Seebeckcoefficient), and anomalous Hall resistivity, respectively. The firstterm on the right-hand side of Equation (1), 𝜌xx𝛼xy (defined asSI), is regarded as an intrinsic component of ANE, where 𝛼xyplays a crucial role. Recent studies have shown that large Berrycurvature originating from topological electronic structures nearAdv. Sci. 2024, 11, 2308543 © 2024 The Authors. Advanced Science published by Wiley-VCH GmbH2308543 (1 of 9)http://www.advancedscience.commailto:zhou.weinan@nims.go.jphttps://doi.org/10.1002/advs.202308543http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadvs.202308543&domain=pdf&date_stamp=2024-03-06www.advancedsciencenews.com www.advancedscience.comFigure 1. Schematic illustrations of a) ANE in a magnetic material, b) SE in a thermoelectric material, and c) direct-contact STTG in a mag-netic/thermoelectric bilayer. Here, the magnetic material is colored in cyan, while the thermoelectric material is colored in gray. The black arrow representsthe direction of M of the magnetic material. L and W in c) are the lengths of the bilayer along the x-axis and y-axis, while tM, tTE, and ttot are the thicknessesof the magnetic material, the thermoelectric material, and the bilayer, respectively. The equivalent circuits of the magnetic/thermoelectric bilayer for d)the effective longitudinal resistivity (𝜌xx ,eff), e) the effective Seebeck coefficient (SSE,eff), and f) the effective anomalous Hall resistivity (𝜌AHE,eff) or theeffective intrinsic contribution to the transverse thermopower (SI,eff).the Fermi level leads to large values of 𝛼xy, which usually resultsin large SANE for these magnetic materials as well. The currentrecord-high SANE > 6 μV K−1 at room temperature has been re-ported for the Weyl semimetal Co2MnGa.[13,25–27] This is a morethan an order of magnitude enhancement of SANE from tradi-tional magnetic materials like Fe, Co, and Ni. Exploring mag-netic materials with large values of 𝛼xy has thus become a majorstrategy for achieving large transverse thermopower.[28–38] Mean-while, the second term on the right-hand side of Equation (1),−SSE𝜌AHE𝜌xx(defined as SII), is due to the anomalous Hall effect(AHE) of a magnetic material acting on the longitudinal chargecurrent induced by its SE. Inspired by SII, recently, a differ-ent approach to enhance the transverse thermopower has beenproposed and demonstrated: referring to as the Seebeck-driventransverse magneto-thermoelectric generation (STTG, see Exper-imental Section), this approach is based on a closed circuit con-sisting of a magnetic material and a thermoelectric material withelectrical connection only at both ends along the direction of∇T.[39–42] Here, the strong SE of the thermoelectric material gen-erates a much larger longitudinal charge current in the magneticmaterial, which is then converted to the transverse direction byits AHE, leading to a significant enhancement of transverse ther-mopower. The value of transverse thermopower is determinedby not only the transport properties of the magnetic and ther-moelectric materials but also their sizes. Quantitative agreementbetween experimental demonstrations and the phenomenolog-ical formulation has been reported. However, the formation ofsuch a closed circuit requires electrical connection only at thetwo ends but insulation in between, which could be a complicatedstructure to be integrated into thermoelectric modules, especiallywhen one tries to reduce the size along the direction of ∇T to playto the advantages of ANE-based modules. A much simpler struc-ture to combine the magnetic and thermoelectric materials andenhance the transverse thermopower would be highly beneficialfor the wide adoption of STTG.In this study, we demonstrate STTG-driven thermopower gen-eration by the simplest way to combine a magnetic material anda thermoelectric material, i.e., stacking a magnetic layer and athermoelectric layer together to form a bilayer (Figure 1a–c). Un-like the closed circuit used in previous studies of STTG, the mag-netic and thermoelectric layers are in direct contact over the en-tire interface. This means that the fabrication of an insulatinglayer between the materials and electrical contacts at both endsto connect the materials is no longer needed, leading to a straight-forward structure. The lack of electrical contacts also eliminatestheir potential shunting effect on the transverse thermopower.Therefore, the direct-contact STTG can be much easier to fabri-cate and much more versatile to be applied to different lengthscales and configurations of thermoelectric modules. We modelthe magnetic/thermoelectric bilayer and derive the expressionsfor its transport properties, which vary with the thickness of thelayers. To experimentally verify the expressions, we characterizea series of samples, which are prepared by depositing Fe–Ga al-loy thin films of various thicknesses onto n-type Si substrates.Here, the Fe–Ga films serve as the magnetic material, and the Sisubstrates serve as the thermoelectric material. The tendencies oftransport properties predicted by the expressions are nicely repro-duced by the measured results. The transverse thermopower ob-tained from the sample with optimized layered structure reaches15.2 ± 0.4 μV K−1, which is a fivefold increase from that of theFe–Ga alloy (SANE = 2.4 ± 0.2 μV K−1) and even larger than thepredicted maximum of 11.4 μV K−1, indicating an additional con-tribution originated from the interface. Our results shed light ona novel and powerful approach for realizing large transverse ther-mopower by combining magnetic and thermoelectric materials.2. Results and DiscussionFigure 1c depicts the bilayer model used in this study, where themagnetic layer is colored in cyan and the thermoelectric layer inAdv. Sci. 2024, 11, 2308543 © 2024 The Authors. Advanced Science published by Wiley-VCH GmbH2308543 (2 of 9) 21983844, 2024, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202308543 by Cochrane Japan, Wiley Online Library on [15/05/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comcolored in gray. Both layers have the same length L (W) along thex-axis (y-axis), while the thicknesses of the magnetic layer, ther-moelectric layer, and bilayer are tM, tTE, and ttot, respectively. Inorder to better facilitate the formulation as well as the exhibitionof the results, we also define a fraction F = tTEttotto represent thethickness ratio, which would take a value between 0 and 1. Weconsider the transverse thermopower of the bilayer to be paral-lel to the y-axis, which happens when ∇T is applied parallel tothe x-axis and M of the magnetic material is parallel to the z-axis.For simplicity, we assume that both tM and tTE are much smallerthan L and W. This means that the change of electrical potentialalong the z-axis would be much smaller than that in the x-y plane,and can be ignored when considering the transport properties inthe x-y plane. Therefore, we can regard the bilayer as a singlehybrid material effectively, and use one parameter to representthe total transverse thermopower (Sytot). However, this limitationon the thicknesses of the layers can be circumvented, which willbe discussed later. Sytot can be formulated by mimicking Equa-tion (1) with the parameters on the right-hand side replaced bythe effective parameters representing the transport properties ofthe bilayer. These effective parameters can be derived by consider-ing the bilayer as two conductors (representing the magnetic andthermoelectric layers) connected in parallel. Figure 1d shows theequivalent circuit for the effective longitudinal resistivity (𝜌xx,eff)of the bilayer along the x-axis. Here, RxM and RxTE are the resis-tance of the magnetic and thermoelectric layers along the x-axis,respectively. 𝜌xx,eff can be expressed as𝜌xx,eff =𝜌M𝜌TEF𝜌M + (1 − F) 𝜌TE(2)where 𝜌M and 𝜌TE are the longitudinal resistivity of the magneticand thermoelectric layers, respectively. 𝜌xx,eff is assumed to beisotropic in the x-y plane. Figure 1e shows the equivalent circuitfor the effective Seebeck coefficient (SSE,eff) of the bilayer alongthe x-axis. Here, the two power source symbols represent theelectrical potential due to the SE of the magnetic layer (equalto SML∇T) and the thermoelectric layer (equal to STEL∇T), withSM and STE representing the Seebeck coefficient of the magneticand thermoelectric materials, respectively. Hence, SSE,eff can beexpressed asSSE,eff =(STE − SM) F𝜌MF𝜌M + (1 − F) 𝜌TE+ SM (3)It is worth mentioning that Equations (2) and (3) are equivalentto the expressions presented in previous reports that study SEof multilayer systems.[43–45] As for the effective anomalous Hallresistivity (𝜌AHE,eff) and the effective SI (SI,eff) of the bilayer alongthe y-axis, their equivalent circuits take a similar form, as shownin Figure 1f. Since there is no transverse effect in a thermoelectricmaterial under zero magnetic field, the power source symbol onlyexists in the magnetic layer, which equals to 𝜌AHEUW𝜌ML(SIW∇T) incase of 𝜌AHE,eff (SI,eff). Here, U is the electrical potential applied tothe bilayer along the x-axis. Then, 𝜌AHE,eff can be expressed as𝜌AHE,eff =𝜌AHE (1 − F) 𝜌2TE(F𝜌M + (1 − F) 𝜌TE)2(4)while SI,eff can be expressed asSI,eff = SI(1 − F) 𝜌TEF𝜌M + (1 − F) 𝜌TE(5)Using these effective parameters described in Equations (2–5),we finally obtain the expression for Sytot asSytot = SI,eff − SSE,eff𝜌AHE,eff𝜌xx,eff=(1 − F) 𝜌TEF𝜌M + (1 − F) 𝜌TE(SANE −F𝜌AHEF𝜌M + (1 − F) 𝜌TE(STE − SM))(6)The part inside the large bracket on the right-hand side ofEquation (6), interestingly, is equivalent to the expression for thetotal transverse thermopower of a closed circuit, with the secondterm inside the large bracket being the STTG term.[39] Previousstudies have shown that in a closed circuit consisting of magneticand thermoelectric materials, the total transverse thermopowerincreases with increasing proportion of thickness of the thermo-electric material (which equals to F→ 1).[39–42] On the other hand,the part outside the large bracket of Equation (6) decreases withincreasing F, when F is between 0 and 1. This indicates that Sytotstudied here would behavior differently comparing to that of aclosed circuit.In order to illustrate the behavior of Sytot, we calculated Sytot asa function of F using Equation (6) for different combinations ofmagnetic and thermoelectric materials. Co2MnGa, Fe–Ga alloy,and Ni are chosen as the magnetic materials to represent differ-ent values in 𝜌AHE, while n-type Si and Bi2Te2.7Se0.3 are chosenas the thermoelectric materials to represent different values in𝜌TE and STE. The transport properties of Co2MnGa,[13] Ni,[46] andBi2Te2.7Se0.3[47] are extracted from literature, while the transportproperties of Fe–Ga and Si are experimentally measured in thisstudy and will be described in detail later. Figure 2a shows theresults when Si (STE = −0.91 mV K−1, 𝜌TE = 37.8 mΩ cm) is thethermoelectric material. Here, the value of Sytot at F = 0 corre-sponds to SANE of the magnetic materials, which changes withincreasing F and reaches a peak at a certain value of F, beforeit eventually diminishes to 0. When Co2MnGa is the magneticmaterial, the maximum Sytot can be up to 30 μV K−1, a significantenhancement from SANE of Co2MnGa (= 6 μV K−1), owing to itslarge 𝜌AHE of 15 μΩ cm. On the other hand, due to the small neg-ative 𝜌AHE of Ni (= −0.045 μΩ cm), the STTG term becomes neg-ative, and Sytot peaks in the negative region with small magnitude.Another feature here is that the values of F for Sytot to reach thepeaks are very close to 1, i.e., a large proportion of thickness of thebilayer is the thermoelectric material. This is due to the fact that𝜌TE is much larger than 𝜌M. In contrast, in the case of Bi2Te2.7Se0.3(STE = −0.19 mV K−1, 𝜌TE = 1.0 mΩ cm) being the thermoelec-tric material (Figure 2b), the values of F for Sytot to reach the peaksare clearly smaller, since 𝜌TE for Bi2Te2.7Se0.3 is over an order ofmagnitude smaller than that of Si and much closer to 𝜌M. Theenhancement in Sytot is less significant comparing to the resultsin Figure 2a, due to STE for Bi2Te2.7Se0.3 being much smaller inmagnitude than that of Si; still, over 30% enhancement can beachieved for the bilayers containing Co2MnGa and Fe–Ga. Thecalculated results reveal the importance of strong AHE for theAdv. Sci. 2024, 11, 2308543 © 2024 The Authors. Advanced Science published by Wiley-VCH GmbH2308543 (3 of 9) 21983844, 2024, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202308543 by Cochrane Japan, Wiley Online Library on [15/05/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 2. a) Sytot as a function of F calculated using Equation (6) for the bi-layers of Co2MnGa/Si, Fe–Ga/Si, and Ni/Si. The inset shows the magnifiedview of the lines in the range of F between 0.96 and 1. b) Sytot as a function ofF calculated using Equation (6) for the bilayers of Co2MnGa/Bi2Te2.7Se0.3,Fe–Ga/Bi2Te2.7Se0.3, and Ni/Bi2Te2.7Se0.3.magnetic material, strong SE for the thermoelectric material, andan optimal thickness ratio of the bilayer, for realizing a significantenhancement in transverse thermopower.To verify the expressions for the transport properties ofthe magnetic/thermoelectric bilayer and demonstrate large Sytotthrough direct-contact STTG, we prepared and systematicallystudied a series of samples with different F values. Figure 3ashows a cross-sectional schematic view of these samples. Weused a Silicon-on-Insulator (SOI) substrate, which consists of twoSb-doped n-type Si layers separated by a 1-μm-thick SiO2 insu-lator. The top Si layer with tTE = 20 μm serves as the thermo-electric layer; the bottom 550-μm-thick Si acts as the support forthe bilayer. After cleaning the surface of the top Si layer, we de-posited the magnetic layer of Fe-Ga alloy thin films with variousthicknesses (tM = 10, 20, 40, 70, 100, 150, 200, 350, and 500 nm)at room temperature by magnetron sputtering. The Fe–Ga filmserves as the magnetic layer, which is selected for its large 𝜌AHEand minimal thickness dependence of the transport properties,as reported in a previous study.[41] The samples were then cappedwith 2-nm-thick Au layers to prevent oxidation (see ExperimentalSection for details). The composition of the Fe–Ga films was de-termined to be Fe70Ga30 by wavelength dispersive X-ray fluores-cence (XRF) analysis. To obtain the transport properties of n-typeSi and Fe–Ga, we also carried out measurements on the bare SOIsubstrate as well as on a reference sample of 100-nm-thick Fe-Gafilm deposited on a thermally oxidized Si substrate. The sampleswere cut into a smaller size of L = 10 mm and W = 5 mm priorto the transport measurements. Figure 3b,c shows the measure-ment setups to evaluate the electrical (𝜌xx ,eff and 𝜌AHE,eff) and ther-moelectric (SSE,eff and Sytot) transport properties of the samples atroom temperature (see Experimental Section for details). Fromthe bare SOI substrate, 𝜌TE was measured to be 37.8 ± 0.8 mΩ cmwhile STE was measured to be −0.91 ± 0.06 mV K−1. Figure 3d–fshows the transverse resistivity (𝜌yx) as a function of out-of-planemagnetic field (H) for the samples with tM = 20, 70, and 200 nm,respectively; while Figure 3h–j shows the transverse electric field(Ey) divided by ∇T as a function of H for these samples. The re-sults obtained from the Fe-Ga reference sample are displayed inFigure 3g,k for comparison (see the results from the rest of thesamples in Figures S1 and S2, Supporting Information). All thecurves show H-odd dependence, as well as saturation of signalsabove μ0H ≈ 1.2 T, which corresponds to M of Fe–Ga aligned tothe direction of H. However, the slopes of the curves at high Hafter saturation are different among the samples, especially com-pared to that of the reference sample being almost horizontal.These slopes are mainly due to the ordinary Hall effect (OHE) andordinary Nernst effect (ONE) of n-type Si, which manifest them-selves as transverse signals changing linearly with increasing H.On the other hand, the OHE and ONE of the Fe–Ga film are ne-glectable compared to their anomalous counterparts, as shownin Figure 3g,k. For samples with small tM, the n-type Si plays amore important role in determining the overall transport proper-ties, and the OHE and ONE are more prominently displayed inthe transverse signals under high H; for samples with large tM,the Fe–Ga film plays a more important role, while the OHE andONE of n-type Si are shunted by the Fe–Ga. However, since ourinterests are the anomalous components of the transport prop-erties, we evaluated 𝜌AHE,eff and Sytot by extrapolating the curvesat high H after saturation down to zero H, as indicated by thedashed black lines in Figure 3d,h. On the other hand, from the re-sults of the Fe–Ga reference sample (Figure 3g,k), 𝜌AHE and SANEare evaluated to be 6.1 ± 0.1 μΩ cm and 2.4 ± 0.2 μV K−1, re-spectively. 𝜌M was measured to be 135 ± 3 μΩ cm while SM wasmeasured to be −19.2 ± 1.7 μV K−1 under zero H. These trans-port properties of Fe–Ga are consistent with previously reportedresults.[41,48]Using the measured transport properties of n-type Si and Fe–Ga as well as the derived expressions, we calculated 𝜌xx ,eff, SSE,eff,𝜌AHE,eff, and Sytot as a function of F based on Equations (2–4) and(6), shown as the curves in Figure 4a–d. Here, the insets show thecalculated curves in the full range of F between 0 and 1; the valuesat F = 0 correspond to the transport properties of Fe–Ga, whilethe values at F = 1 correspond to those of n-type Si. The mainfigures focus on the range of F between 0.96 and 1, where thechanges are more prominent. The results measured from the Fe–Ga/Si samples are plotted as data points at the corresponding Ffor comparison. Regarding 𝜌xx ,eff, the experimental result clearlyshows a monotonic increase with increasing F toward 1, which isin quantitative agreement with the calculated result (Figure 4a).A quantitative agreement can also be seen for SSE,eff in Figure 4b,where the values decrease with increasing F toward 1 for both theexperimental and calculated results. In contrast, 𝜌AHE,eff and Sytotbehave quite differently: the calculated results suggests that bothAdv. Sci. 2024, 11, 2308543 © 2024 The Authors. Advanced Science published by Wiley-VCH GmbH2308543 (4 of 9) 21983844, 2024, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202308543 by Cochrane Japan, Wiley Online Library on [15/05/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 3. Schematic illustrations of a) a cross-sectional view of the samples, b) the electrical transport measurement setup, and c) the thermoelectrictransport measurement setup. Here, V1 and V2 represent two nanovoltmeters measuring the longitudinal and transverse signals, respectively. The blackink layer in c) is for evaluating ∇T using an infrared camera. d) H dependence of 𝜌yx of the sample with tM = 20 nm, e) tM = 70 nm, f) tM = 200 nm,and g) the reference sample for the Fe–Ga alloy. h) H dependence of Ey divided by ∇T of the sample with tM = 20 nm, i) tM = 70 nm, j) tM = 200 nm,and k) the reference sample. The dashed black lines in d) and h) indicate the linear fitting at high H to evaluate 𝜌AHE,eff and Sytot at zero H.would reach their maximum at certain values of F, more specifi-cally, F = 0.9964 for 𝜌AHE,eff to peak at 431 μΩ cm while F = 0.9960for Sytot to peak at 11.4 μV K−1 (Figure 4c,d). These tendencies arewell reproduced by the experimental results. However, the peakvalues for both 𝜌AHE,eff and Sytot are even larger: 𝜌AHE,eff reaches595 ± 9 μΩ cm at F = 0.9980 (tM = 40 nm) while Sytot reaches 15.2± 0.4 μV K−1 at F = 0.9965 (tM = 70 nm). One can clearly seethat the deviations between the experimental and calculated re-sults for 𝜌AHE,eff and Sytot are prominent when F is close to 1, i.e.,for samples with tM ≤ 100 nm. This suggests that the Fe–Ga/Siinterface could be a factor to these deviations since the interfacecould have a more significant influence when tM is small. It is alsoworth pointing out that while 𝜌AHE,eff enhanced significantly to al-most two orders of magnitude larger than 𝜌AHE at the peak value,the effective anomalous Hall angle of the bilayer monotonicallydecreases with increasing F toward 1 (Figure S3a, Supporting In-formation). Meanwhile, the agreement between the experimentaland calculated results indicates that the change in electronic bandstructures of Fe–Ga and Si is insignificant due to the formationof a bilayer, with a possible exception for the Fe–Ga/Si interface.Overall, the measured transport properties verify the derived ex-pressions for the magnetic/thermoelectric bilayer, and demon-strate that direct-contact STTG can indeed significantly enhancethe transverse thermopower when magnetic and thermoelectricmaterials are combined properly.To study the interface between the Fe–Ga and Si layers, weperformed scanning transmission electron microscopy (STEM)analysis on the bilayer samples. The results for the sample withtM = 70 nm are summarized in Figure 5. The high-angle annu-lar dark-field STEM (HAADF-STEM) image in Figure 5a shows acontinuous and flat Fe–Ga layer deposited on the SOI substrate.Based on the energy dispersive X-ray spectroscopy (EDS) map-ping of the relevant elements and the corresponding line com-position profile along the out-of-plane direction of the sample inFigure 5a,b, most of the Fe–Ga layer has a uniform compositionof Fe:Ga = 7:3, which is consistent with the result obtained byXRF analysis, while one can see Ga-rich regions on a part of thelayer’s top surface. (Note that the slight increase in Ga compo-sition at the top surface of the Fe–Ga layer was not observed inthe sample with tM = 20 nm as shown in Figure S4, Support-ing Information.) The selected area electron diffraction (SAED)pattern of the Fe–Ga layer (Figure 5c) shows a concentric ringpattern that can be well indexed as a body-centered cubic struc-ture with no clear superlattice reflections from ordered Fe–GaAdv. Sci. 2024, 11, 2308543 © 2024 The Authors. Advanced Science published by Wiley-VCH GmbH2308543 (5 of 9) 21983844, 2024, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202308543 by Cochrane Japan, Wiley Online Library on [15/05/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 4. a) 𝜌xx ,eff as a function of F, which is the ratio of tTE to ttot, in the range between 0.96 and 1. The green line is calculated using Equation (2) withthe experimentally measured transport properties of Fe-Ga and n-type Si, while the green data points are measured from the samples with various tM aslabeled on the points. The inset shows the calculated line in the full range of F between 0 and 1. b) SSE,eff as a function of F. The purple line is calculatedusing Equation (3), while the purple data points are measured from the samples. The inset shows the calculated line in the full range. c) 𝜌AHE,eff as afunction of F. The cyan line is calculated using Equation (4), while the cyan data points are measured from the samples. The inset shows the calculatedline in the full range. d) Sytot as a function of F. The red line is calculated using Equation (6), while the red data points are measured from the samples.The inset shows the calculated line in the full range. The calculated red line is the same as the red line in Figure 2a.phases, suggesting the Ga atoms randomly substitute the Fe lat-tice. The SAED pattern also shows that the Fe–Ga layer consists ofrandomly oriented polycrystalline grains. Figure 5d,e shows thehigh-resolution HAADF-STEM image, EDS mapping, and cor-responding line composition profile across the Fe–Ga/Si inter-face. There is an approximately 2-nm-thick amorphous-like layerwith dimly imaging contrast consisting of Si and Fe between thebrightly imaged crystalline Fe–Ga layer and the darkly imaged Silayer. A similar Fe–Ga/Si interface was observed for the samplewith tM = 20 nm (Figure S4, Supporting Information). While notconsidered during the formulation of the expressions, this inter-facial layer could contribute positively to 𝜌AHE,eff and Sytot, due tothe emergence of spin-orbit coupling at the interface or ferromag-netic surface state of FeSi.[49,50] If the thicknesses of the bilayersare increased, it is possible that the interfacial layer would havea less significant influence on the transport properties, leadingto a better agreement between the experimental and calculatedresults. On the other hand, if the thicknesses of the bilayers areincreased to a level that they are comparable to the sample size inthe x-y plane (L and W), the assumption for the modeling is nolonger satisfied and the derived expressions cannot accurately de-scribe the transverse thermopower of the bilayers. The enhance-ment of ANE due to the contribution from the interfaces has beenpreviously reported for multilayer structures.[51–53] Creating mul-tilayer samples of magnetic and thermoelectric materials, whichhave a certain value of F but various numbers of interfaces, couldbe a helpful way to isolate the effect originating from the inter-face.Up to this point, we have been focusing on mag-netic/thermoelectric bilayers. However, the derived expressionshold true for multilayer structures consisting of magnetic andthermoelectric materials. In such a case, the thickness of thewhole multilayer can be on the same length scale as W andL, as long as the thicknesses of the individual magnetic andthermoelectric layers are much smaller than W and L, while Fwould be the ratio of the total thickness of thermoelectric layersto the thickness of the whole multilayer. Equation (6) can thenbe used to estimate the maximum Sytot of a certain combinationof magnetic and thermoelectric materials, as well as the bestthickness ratio to combine the two materials. It is also worthmentioning that Sytot in direct-contact STTG is determined byM of the magnetic material, the same as in ANE. Therefore,the current magnetic/thermoelectric bilayer can achieve TTGunder zero external magnetic field if the magnetic material hasanisotropy and is able to maintain M perpendicular to both ∇Tand the generated E, such as with L10-FePt[39] or SmCo5.[54]Adv. Sci. 2024, 11, 2308543 © 2024 The Authors. Advanced Science published by Wiley-VCH GmbH2308543 (6 of 9) 21983844, 2024, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202308543 by Cochrane Japan, Wiley Online Library on [15/05/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comFigure 5. a) Cross-sectional HAADF-STEM image of the sample with tM = 70 nm, together with the EDS elemental maps of Si, Fe, Ga, Au, and Pt, andb) the corresponding line composition profile along the direction as indicated by the white dashed arrow in a). Pt was deposited during the making ofthe STEM specimen. c) SAED pattern of the Fe–Ga layer in a). d) HAADF-STEM image of the same sample focusing on the Fe–Ga/Si interface, togetherwith the EDS elemental maps of Si, Fe, and Ga, and e) the corresponding line composition profile along the direction as indicated by the white dashedarrow in d).3. ConclusionWe have explored the simplest way to combine magnetic andthermoelectric materials, and demonstrated its potential to sig-nificantly enhance the transverse thermopower. We considereda model of simply stacking magnetic and thermoelectric layers,and derived the expressions for the transport properties of thehybrid structure, which varies with thickness of the layers. Usingthe Fe–Ga alloy as the magnetic material and n-type Si as the ther-moelectric material, the expressions predict Sytot to reach a peakvalue up to 11.4 μV K−1 at a certain thickness ratio (F = 0.9960),which is a significant enhancement from SANE = 2.4 ± 0.2 μVK−1 of the Fe–Ga alloy, and much larger than the current record-high SANE in a single material (Co2MnGa) at room temperature.To experimentally verify this prediction, we prepared a series ofsamples by depositing Fe–Ga alloy thin films of various thick-nesses onto n-type Si substrates, and measured their transportproperties. The measured results agree well with all the derivedexpressions, reproduced the predicted tendency of Sytot with aneven larger value of 15.2 ± 0.4 μV K−1 at F = 0.9965. The addi-tional contribution to Sytot may be originated from the Fe–Ga/Siinterface. Our results demonstrate that combining magnetic andthermoelectric materials, even in the form as simple as stackingthem together into a bilayer, can be a powerful approach for en-hancing Sytot. With a great number of studies reporting on dif-ferent magnetic and thermoelectric materials, the exploration oftheir combinations with direct-contact STTG could lead to dis-coveries of composite materials with excellent properties, whichwill propel the wide adoption of transverse thermoelectric appli-cations.4. Experimental SectionSeebeck-Driven Transverse Magneto-Thermoelectric Generation: Al-though in previous studies, the phenomenon has been referred to asSeebeck-driven transverse thermoelectric generation, to prevent confu-sion with other types of TTG solely associated with the SE and emphasizethe key role of magnetic materials, we added magneto- to the name of thephenomenon. The acronym for the phenomenon is retained as STTG.Formulation: The effective anomalous Hall angle (tan𝜃AHE,eff) of thebilayer can be formulated based on 𝜌xx ,eff and 𝜌AHE,eff, and is given bytan 𝜃AHE,eff = tan 𝜃AHE(1 − F) 𝜌TEF𝜌M + (1 − F) 𝜌TE(7)where tan 𝜃AHE = 𝜌AHE𝜌Mis the anomalous Hall angle of the magnetic mate-rial. Figure S3a (Supporting Information) shows tan𝜃AHE,eff as a functionof F, where the tendency of results measured from the Fe–Ga/Si samplesagrees with the calculation based on Equation (7). With the expressionsfor Sytot and 𝜌xx ,eff, we can define the power factor (PF) for TTG of the mag-netic/thermoelectric bilayer asPF =Sytot2𝜌xx,eff(8)In addition, the effective thermal conductivity (𝜅xx ,eff) of the bilayer inthe x-y plane can also be derived, by considering it as two thermal conduc-Adv. Sci. 2024, 11, 2308543 © 2024 The Authors. Advanced Science published by Wiley-VCH GmbH2308543 (7 of 9) 21983844, 2024, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202308543 by Cochrane Japan, Wiley Online Library on [15/05/2024]. 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.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comtors (representing the magnetic and thermoelectric layers) connected inparallel. Thus, 𝜅xx ,eff can be expressed as𝜅xx,eff = (1 − F) 𝜅M + F𝜅TE (9)where 𝜅M and 𝜅TE are the thermal conductivity of the magnetic and ther-moelectric materials, respectively. Then, the isothermal figure of merit forTTG (zxyT) of the bilayer can be expressed aszxyT =Sytot2T𝜌xx,eff𝜅xx,eff(10)following the definition used by Delves.[55,56]Sample Preparation: The Fe–Ga/Si bilayer samples were prepared bydepositing the Fe–Ga films onto the SOI substrates. As shown in Figure 3a,the SOI substrates consist of two Sb-doped n-type Si layers separated bya 1-μm-thick SiO2 layer, where the 20-μm-thick top Si layer serves as thethermoelectric layer. To ensure a good electrical connection between theFe–Ga film and the top Si layer, Ar-ion milling was performed to removethe oxidation layer on top of Si before deposition. Then, without break-ing the vacuum, the SOI substrates were transferred to another chamber,where the Fe–Ga films were deposited from a single Fe65Ga35 alloy targetby magnetron sputtering at room temperature. The thicknesses of the Fe–Ga films were varied (tM = 10, 20, 40, 70, 100, 150, 200, 350, and 500 nm)by controlling the deposition time. The 2-nm-thick Au capping layers weredeposited subsequently to prevent oxidation. The Fe–Ga reference sam-ple was prepared by depositing a 100-nm-thick Fe–Ga film on a thermallyoxidized Si substrate, which was also capped by a 2-nm-thick Au cappinglayer. Before the transport measurements, all the samples were cut into asmaller size of L = 10 mm and W = 5 mm. All four edges of the samplesare either newly cut or covered by sample holders during deposition, toensure that there is no metallic film on the edges to electrically connectthe top and bottom Si layers.Transport Measurements: The longitudinal and transverse resistivitiesof the samples were measured using a Physical Property MeasurementSystem (PPMS) together with its standard resistivity puck. The sampleswere set on a puck and wire bonding was used to connect the samplesto the electrodes on the puck, with the configuration shown in Figure 3b.The electrical connections were fed into external electronics. The powersource in Figure 3b represents a Keithley 2401 sourcemeter, while V1 andV2 represent two Keithley 2182A nanovoltmeters. H was swept along theout-of-plane direction by the PPMS during the measurement. The longitu-dinal and transverse thermopower of the samples was measured using ahomemade holder embedded in a multi-function probe together with thePPMS, as the sample configuration shown in Figure 3c. The homemadeholder contains a Peltier module to generate a stable ∇T across the sam-ple plane. During the measurement, a constant electrical current (I=±1.0,±0.8, or ±0.6 A) was applied to the Peltier module, which corresponded to−0.8 K mm−1 <∇T< 0.8 K mm−1 when the sample reached a steady state.A portion of the surfaces of the samples were coated by black ink having aknown emissivity of 0.94, in order to evaluate ∇T using an infrared camera.The details of the home-made holder and the measurement procedure aredescribed in a previous paper.[39] The images taken by the infrared camerawere also used to evaluate the distances between electrical connections forcalculating the parameters. All the transport measurements were carriedout at room temperature.Scanning Transmission Electron Microscopy Measurement: The electrontransparent thin lamella specimens were prepared by standard focusedion beam (FIB) lift-out technique using an FEI Helios G4 UX system. TheSTEM-EDS analysis was performed using an FEI Titan G2 80–200 trans-mission electron microscope operating at 200 kV.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThe authors thank S. Kasai and M. Maeda for their support in samplepreparation and characterization. This work was supported by JST ERATO“Magnetic Thermal Management Materials” (Grant No. JPMJER2201) andJSPS KAKENHI Grants-in-Aid for Research Activity Start-up (Grant No.JP22K20494).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 Hall effect, anomalous Nernst effect, Seebeck effect, spincaloritronics, transverse thermoelectric generationReceived: November 8, 2023Revised: January 7, 2024Published online: March 6, 2024[1] G. J. Snyder, E. S. Toberer, Nat. 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Phys. Lett.2019, 115, 222403.[55] R. T. Delves, Br. J. Appl. Phys. 1964, 15, 105.[56] M. R. Scudder, K. G. Koster, J. P. Heremans, J. E. Goldberger, Appl.Phys. Rev. 2022, 9, 021420.Adv. Sci. 2024, 11, 2308543 © 2024 The Authors. Advanced Science published by Wiley-VCH GmbH2308543 (9 of 9) 21983844, 2024, 18, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202308543 by Cochrane Japan, Wiley Online Library on [15/05/2024]. 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.advancedscience.com Direct-Contact Seebeck-Driven Transverse Magneto-Thermoelectric Generation in Magnetic/Thermoelectric Bilayers 1. Introduction 2. Results and Discussion 3. Conclusion 4. Experimental Section Supporting Information Acknowledgements Conflict of Interest Data Availability Statement Keywords