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[ODSE_SmCo-BST_EES2025_SI.pdf](https://mdr.nims.go.jp/filesets/855d2f34-4265-4046-b9bf-e78b74188abb/download)

## Creator

[Fuyuki Ando](https://orcid.org/0009-0003-7789-8170), [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), [Abdulkareem Alasli](https://orcid.org/0000-0002-1681-0492), [Hossein Sepehri-Amin](https://orcid.org/0000-0002-7856-7897), [Yutaka Iwasaki](https://orcid.org/0000-0002-7317-4939), Hosei Nagano, [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051)

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[Multifunctional composite magnet realizing record-high transverse thermoelectric generation](https://mdr.nims.go.jp/datasets/6501a255-8b01-43a0-ad15-2ea7491f86c8)

## Fulltext

1   Supplementary information  Multifunctional composite magnet realizing record-high transverse thermoelectric generation  Fuyuki Ando,*a Takamasa Hirai,a Abdulkareem Alasli,b Hossein Sepehri-Amin,a Yutaka Iwasaki,a  Hosei Naganob and Ken-ichi Uchida*ac  a. National Institute for Materials Science, Tsukuba 305-0047, Japan b. Department of Mechanical Systems Engineering, Nagoya University, Nagoya 464-8603, Japan c. Department of Advanced Materials Science, Graduate School of Frontier Sciences,  The University of Tokyo, Kashiwa 277-8561, Japan *E-mail: ANDO.Fuyuki@nims.go.jp; UCHIDA.Kenichi@nims.go.jp   Supplementary Information (SI) for Energy & Environmental Science.This journal is © The Royal Society of Chemistry 2025mailto:ANDO.Fuyuki@nims.go.jpmailto:UCHIDA.Kenichi@nims.go.jp  2  Note S1. Observation of nonuniform charge-to-heat current conversion in MCM To buttress the appearance of the transverse thermoelectric conversion, we measured the charge-current-induced temperature modulation in SmCo5/BST-based MCM by using the LIT technique. The application of Jc induces a net heat current Jq in the orthogonal direction by the off-diagonal Peltier effect, which is the Onsager reciprocal of ODSE.1 We performed LIT measurements at Jc = 1 A and various f values in the cross-sectional and top-side configurations, as shown in Fig. S1a,b, and obtained A and  images using Enhanced Lock-In Thermal Emission (ELITE, DCG Systems G.K.) at room temperature and atmospheric pressure. The SmCo5/BST-based MCM with 𝜃 = 25° and dimensions of 2.2  11.7  2.0 mm was used for the LIT measurements. The procedures of the mounting and surface coating of the sample were the same as the experiments in Fig. 3f and Experimental section in the main text. Fig. S1c–f shows the results of the LIT measurements. In the cross-sectional configuration, the A and  images at f = 10.0 Hz indicate that alternating heating and cooling signals are localized near the SmCo5/BST interfaces in a similar manner to that shown in Fig. 3f in the main text. Importantly, the magnitude of the A signals for θ = 25° was nonuniform along the oblique interfaces because the charge current flowed nonuniformly due to the anisotropic electrical conductivity; this is the origin of transverse thermoelectric conversion by the off-diagonal Peltier effect. These local heating and cooling signals were broadened through thermal diffusion as f decreased. The A image at f = 0.1 Hz, showing a nearly steady-state amplitude of the temperature modulation, indicates that large temperature changes occurred near the upper and lower edges of the sample. The  signals varied from approximately 0° (red regions) to 180° (blue regions) in the direction perpendicular to Jc, indicating transverse thermoelectric heating and cooling, respectively.1 This behavior is more evident in the results for the top-side configuration. Fig. S1e,f shows that almost uniform  signals of approximately 180° are induced by the longitudinal charge current at f = 0.1 Hz, confirming that SmCo5/BST-based MCM operates as a transverse thermoelectric converter. Fig. S1g shows the line profiles of the average temperature modulation signals in the area defined by the white dotted rectangles in Fig. S1e,f, where the A signals periodically change due to the multilayer structure. Our MCM exhibited a considerably larger temperature modulation of 1–2 K at f = 0.1 Hz than that in the previously reported Nd2Fe14B/Bi88Sb12-based ATMLs (approximately 0.2 K) with the same Jc and f values.1 The observation of the large off-diagonal Peltier effect ensures that our MCM exhibits large transverse thermoelectric generation by ODSE.    3  Note S2. Calculation of thermoelectric parameters in MCM The thermoelectric parameters, i.e., electrical resistivity ρij, thermal conductivity κij, and thermopower Sij, for SmCo5/BST-based ATML are calculated based on Goldsmid’s method as follows: 𝜌𝑥𝑥 = 𝜌||cos2𝜃 + 𝜌⊥sin2𝜃 (1) 𝜌𝑦𝑦 = 𝜌||sin2𝜃 + 𝜌⊥cos2𝜃 (2) 𝜌x𝑦 = (𝜌|| − 𝜌⊥) sin 𝜃 cos𝜃 (3) 𝜅𝑥𝑥 = 𝜅||cos2𝜃 + 𝜅⊥sin2𝜃 (4) 𝜅𝑦𝑦 = 𝜅||sin2𝜃 + 𝜅⊥cos2𝜃 (5) 𝜅𝑥𝑦 = (𝜅|| − 𝜅⊥) sin 𝜃 cos 𝜃 (6) 𝑆𝑥𝑥 = 𝑆||cos2𝜃 + 𝑆⊥sin2𝜃 (7) 𝑆𝑦𝑦 = 𝑆||sin2𝜃 + 𝑆⊥cos2𝜃 (8) 𝑆𝑥𝑦 = (𝑆|| − 𝑆⊥) sin 𝜃 cos 𝜃 (9) where ρ||, κ||, and S|| (ρ⊥, κ⊥, and S⊥) are the thermoelectric parameters of the SmCo5/BST multilayers in the direction parallel (perpendicular) to the stacking plane. The thickness ratio t and tilt angle θ dependences of the thermoelectric parameters for SmCo5/BST-based ATML, which are obtained by substituting the measured properties of SmCo5 and BST into eqn (1)–(9), are shown in Fig. 2b–d in the main text and Fig. S3. Note S3. Influence of magnetic state on intrinsic thermoelectric performance of MCM The magnetic state of SmCo5 does not contribute to the transverse thermoelectric generation performance in our MCM-based module for the following reasons. Based on the transport measurement results in the magnetized and demagnetized states of SmCo5,1,2 the modulation of ρ and S are 0.2% and 2.9%, respectively. Because Sxy of our MCM is predominantly determined by BST, the modulation of ODSE through the magnetoresistance and magneto-Seebeck effects was estimated to be less than 0.6%. The electric fields induced by the ordinary Nernst effect in BST and ANE in SmCo5 can appear only in the cross-product direction of the x- and y-axes due to the strong magnetic anisotropy of SmCo5 in the stacking direction (Fig. 2a in the main text) so that they are not superposed on the thermopower in the x-axis.    4  Note S4. Calculation of thermoelectric generation performance of MCM-based module We calculated the T dependence of Voc, Rmodule, Pmax, and conversion efficiency η of our MCM-based module using the temperature dependence of analytically calculated transverse thermoelectric properties in Fig. S4. Snyder’s method3,4 was adopted to accurately calculate η for transverse thermoelectric conversion. By introducing the device figure of merit ZxyT of a transverse thermoelectric generator, η is expressed in the traditional manner as 𝜂 =Δ𝑇𝑇h√1 + 𝑍𝑥𝑦𝑇 − 1√1 + 𝑍𝑥𝑦𝑇 + 𝑇c 𝑇h⁄ (10) where T/Th = (Th - Tc)/Th is the Carnot efficiency with Th(c) being the hot (cold) side temperature and the remaining factor is the reduced efficiency depending on ZxyT. The essential difference between zxyT and ZxyT is that whereas zxyT is defined by Sxy(T), ρxx(T), and κyy(T) at specific T, ZxyT (and η) is calculated from the temperature dependence of Sxy(T), ρxx(T), and κyy(T) from Tc to Th and variable with the applied load current. To exactly calculate η using ZxyT, the temperature-dependent thermoelectric properties with an inclement of 1 K were obtained by the linear interpolation and input to the spreadsheet given in the literature.4 Then, by taking Th and Tc measured by the infrared camera and the dimensions and number of the MCM-elements into account, the T dependence of Voc and Rmodule was analytically calculated as shown in Fig. S6a,b. The relative current density u, which refers to the applied load current divided by the input heat current, was optimized to get the maximum output power Pmax value at each T value for the comparison with our experiment. Fig. S6c shows the result of the analytical calculation for Pmax with the experimental values. The T dependence of the calculated η under the same u value is shown in Fig. S6, where the η value at T = 152 K is estimated to be 2.4% (without any losses) and 1.6% (by multiplying the loss fraction of the measured Pmax to the calculated one in Fig. S6c) in maximum. The corresponding normalized conversion efficiency, where η is divided by the Carnot efficiency for the fair comparison of the thermoelectric generation performance, is in the range of 5.2−7.6% in our MCM-based module. The value is much higher than that of Bi/Cu- and Ni/BST-based ATML modules (3.9% and 3.6%, respectively),5,6 but still lower than that of the longitudinal thermoelectric modules7–13 mainly due to the high thermal conductivity of our MCM. Note that the loss fraction of Pmax can be suppressed simply by elongating the MCM element in the E direction because the shunting effect at the boundaries to the electrodes predominantly decreases Voc and hence Pmax.14,15 Thus, the developments in both the materials performance and device engineering are significant for further improvement in η and thermoelectric applications of MCMs.    5   Fig. S1 Temperature modulation due to transverse thermoelectric conversion in MCM. (a,b) Schematic of the LIT measurements for MCM with θ = 25° in the cross-sectional (a) and top-side (b) configurations. Jq denotes the transverse heat current generated by the off-diagonal Peltier effect in SmCo5/BST-based MCM. (c,d) A (c) and  (d) images in the cross-sectional configuration at f = 10.0 and 0.1 Hz. A (e) and  (f) images in the top-side configuration at f = 10.0 and 0.1 Hz. (g) A and  profiles along the Jc direction at f = 0.1, 1.0, and 10.0 Hz for the areas defined by the white dotted rectangles with a size of 512 × 101 pixels in (e) and (f).   Fig. S2 Thermoelectric properties of SmCo5 and BST. (a–c) Temperature T dependence of the electrical resistivity ρ (a), thermal conductivity κ (b), and Seebeck coefficient S (c) for the SmCo5 and BST slabs.   6   Fig. S3 (a–f) Contour plots of the analytical thermoelectric parameters ρxy (a), ρyy (b), κxx (c), κxy (d), Sxx (e), and Syy (f) for SmCo5/BST-based ATML.    Fig. S4 (a–c) T dependence of the analytical transverse thermoelectric properties of the electrical resistivity in the x-axis ρxx (a), thermal conductivity in the y-axis κyy (b), and off-diagonal Seebeck coefficient Sxy (c) with thickness ratio t = 0.5 and tilt angle θ = 25°.     7   Fig. S5 Low-magnification SEM-EDX observations. (a) SEM-EDX mapping of Sb, Te, and Co for the cross section of the SmCo5/BST multilayer. (b) Line profile of the atomic ratio of Sm, Co, Bi, Sb, and Te across the stacking direction.   Fig. S6 Transverse thermoelectric generation performance of MCM-based module. (a–d) T dependence of Voc (a), internal resistance Rmodule (b), Pmax (c), and conversion efficiency η (d) for the thermopile module composed of the 14 SmCo5/BST-based MCM elements with t = 0.5 and θ = 25°. The orange (red) data points show the analytically calculated (experimentally measured) values. The calculated parameters are obtained by inputting the transverse thermoelectric properties based on Fig. S4 to the spreadsheet given in ref. 4.     8  References 1 K. Uchida, T. Hirai, F. Ando and H. Sepehri-Amin, Adv. Energy Mater., 2024, 14, 2302375. 2 A. Miura, H. Sepehri-Amin, K. Masuda, H. Tsuchiura, Y. Miura, R. Iguchi, Y. Sakuraba, J. Shiomi, K. Hono and K. Uchida, Appl. Phys. Lett., 2019, 115, 222403. 3 D. Michael. Rowe, Thermoelectrics Handbook : Macro to Nano, CRC Press, New York, 2006. 4 G. J. 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