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## Creator

[Takumi Yamazaki](https://orcid.org/0000-0001-5289-8615), [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), [Takashi Yagi](https://orcid.org/0000-0002-2008-872X), [Yuichiro Yamashita](https://orcid.org/0000-0003-1376-0263), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), [Takeshi Seki](https://orcid.org/0000-0003-3195-7051), [Koki Takanashi](https://orcid.org/0000-0003-4813-4641)

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[Quantitative measurement of figure of merit for transverse thermoelectric conversion in <math display="inline">  <mi>Fe</mi>  <mo>/</mo>  <mi>Pt</mi></math> metallic multilayers](https://mdr.nims.go.jp/datasets/d661f74a-d76c-495b-9a9f-f981a202ef47)

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1  Quantitative measurement of figure of merit for transverse thermoelectric conversion in Fe/Pt metallic multilayers  Takumi Yamazaki,1,*,§ Takamasa Hirai,2,†,§ Takashi Yagi,3 Yuichiro Yamashita,3 Ken-ichi Uchida,1,2 Takeshi Seki,1,2,‡ and Koki Takanashi4,5 1 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan  2 National Institute for Materials Science, Tsukuba 305-0047, Japan 3 National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8563, Japan 4 Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan 5 Advanced Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan  * takumi.yamazaki.d5@tohoku.ac.jp † HIRAI.Takamasa@nims.go.jp ‡ takeshi.seki@tohoku.ac.jp § These authors contributed equally to this work.  This study presents a measurement method for determining the figure of merit for transverse thermoelectric conversion (zTT) in thin film forms. Leveraging the proposed methodology, we comprehensively investigate the transverse thermoelectric coefficient (ST), in-plane electrical conductivity (σyy), and out-of-plane thermal conductivity (κxx) in epitaxial and polycrystalline Fe/Pt metallic multilayers. The κxx values of multilayers with a number of stacking repetitions (N) of 200 are lower than those of FePt alloy films, indicating that the multilayer structure effectively contributes to the suppression of κxx. zTT is found to increase with increasing N, which remarkably reflects the N-dependent enhancement of the ST values. Notably, ST and σyy are significantly larger in the epitaxial multilayers than those in the polycrystalline counterparts, whereas negligible differences in κxx are observed between the epitaxial and polycrystalline multilayers. This discrepancy in σyy and κxx with respect to crystal growth is due to the different degree of anisotropy in electron transport between epitaxial and polycrystalline multilayers, and epitaxial growth can lead to an enhancement of zTT in the multilayers. The present measurement technique reveals the transverse thermoelectric properties inherent to multilayers.   I.  INTRODUCTION Transverse thermoelectric conversion refers to the generation of electric field by perpendicularly applying a temperature gradient [1,2]. In contrast to the longitudinal thermoelectric conversion based on the Seebeck effect (SE), which needs three-dimensional serial junctions to achieve high device performance, the transverse thermoelectric conversion has an advantage of a 2  simple device structure without junctions. This simplicity in structure contributes to efficient thermal energy harvesting by minimizing electrical and thermal contact resistance. The anomalous Nernst effect (ANE) [3–7] is a representative transverse thermoelectric phenomenon observed in a magnetic material. Unlike the ordinary Nernst effect [8], which requires a substantial magnetic field to obtain large transverse thermopower, the ANE offers the distinct advantage of generating transverse thermopower under a small magnetic field. It is noteworthy that for magnetic materials with spontaneous magnetization, including permanent magnets, transverse thermopower can be generated in the absence of an external magnetic field [9–11]. The ANE-driven electric field EANE is expressed as 𝐄ANE = 𝑆ANE (𝐌|𝐌|× ∇𝑇) , (1) where SANE is the ANE coefficient, T is the temperature gradient applied to the magnetic material, and M is the magnetization [1]. SANE can be expressed as  𝑆ANE  =  𝜌𝑥𝑥𝛼𝑥𝑦  − 𝜌𝑦𝑥𝛼𝑥𝑥, (2) where ρxx, ρyx, αxx, and αxy refer to the longitudinal resistivity, anomalous Hall resistivity, longitudinal thermoelectric conductivity, and transverse thermoelectric conductivity, respectively [6]. The first term on the right-hand side of Eq. (2) refers to the direct conversion from T to EANE due to αxy, which is attributed to the Berry curvature near the Fermi energy in electronic band structures and/or spin-dependent disorder scattering. On the other hand, the second term on the right-hand side of Eq. (2) originates from the anomalous Hall effect of the longitudinal carrier flow induced by the SE. In addition to the characteristic symmetry of transverse thermoelectric conversion, it has a potential of controlling the sign of EANE by changing the direction of M as shown in Eq. (1), enabling us to construct a thermopile structure within a single magnetic material [12]. Although the ANE possesses distinct advantages over the SE as mentioned above, the improvement of the performance of thermoelectric conversion is a crucial issue to realize practical thermoelectric applications. The performance of the ANE-induced transverse thermoelectric conversion is evaluated using the dimensionless figure of merit zANET (= SANE2σyyT/κxx), where σyy, κxx, and T denote the electrical conductivity along EANE, thermal conductivity along T, and absolute temperature, respectively. For an efficient transverse thermoelectric conversion, it is essential to obtain high SANE, high σyy, and low κxx. Currently, the mainstream of materials research for the ANE is developing materials with high SANE. So far, some topological ferromagnets and non-collinear antiferromagnets have been found to exhibit high SANE values owing to the large Berry curvature near the Fermi level [13–21]. The record-high SANE value above room temperature is 6-8 μV K−1 for Co2MnGa [15,19], and that in low temperature region is 23 μV K−1 at 40 K for UCo0.8Ru0.2Al [20]. These materials also exhibit a large zANET of about 0.5×10−3 at 300 K for Co2MnGa and about 1.6×10−3 at 40 K for UCo0.8Ru0.2Al, which were summarized in Ref. [21]. Permanent magnet SmCo5, which 3  has a unique advantage of operating under zero-magnetic field due to its large remanent magnetization and coercivity, achieves large SANE of 5.6 μV K−1 and zANET of 1.1×10−3 at 572 K [9,22]. Bulk single-crystalline YbMnBi2 shows a large ST of about 3 and 6 μV K−1 at around 170 K, depending on its crystallographic orientation [21]. It also has a large zANET value of about 3×10−3 at around 170 K when a heat flux is applied to a specific crystallographic orientation, which is attributed not only to the substantial SANE but to the layered structure that induces anisotropy in the transport properties [23]. In other words, the anisotropy of the electrical and thermal transport properties plays an important role in enhancing the performance of transverse thermoelectric conversion.  Another promising candidate to achieve high transverse thermopower is multilayers. Several studies have reported that the transverse thermopower can be enhanced by forming the multilayer structures with a number of interfaces [24–29]. It should be noted that in the in-plane magnetized configuration of multilayers, in addition to the ANE, the spin Seebeck effect (SSE) [30–33] and/or the spin-dependent Seebeck effect (SdSE) may affect the transverse thermopower [34]. In the case of multilayers with in-plane magnetized configuration, thus, we rewrite the transverse thermoelectric coefficient to be ST. The SSE and SdSE refer to the heat-to-spin current conversion phenomena in a magnet/heavy metal junction driven by magnon spin current and conduction electron spin current, respectively. When combined with the inverse spin Hall effect in the heavy metal layer [35], these effects exhibit the same thermoelectric conversion symmetry as the ANE in the in-plane magnetized configuration [36]. In the case of the in-plane magnetized configuration, i.e., the direction of electrical conduction (y) is parallel to the in-plane of multilayer, and the direction of heat conduction (x) is perpendicular to the multilayer surface as illustrated in Fig. 1, the inherent structural anisotropy of multilayers is expected to induce the anisotropy of transport properties. That is, one may anticipate that κxx is reduced remarkably by forming the multilayer structure while the reduction of σyy is not so significant, resulting in an enhancement of the dimensionless figure of merit for the transverse thermoelectric conversion zTT (= ST2σyyT/κxx) in multilayers. However, the influence of formation of multilayer on κxx has not experimentally been examined yet using the systematic samples due to the difficulty in the thermal conductivity measurements for thin films. Moreover, the quantitative evaluation for ST is not established for thin film samples with the in-plane magnetized configuration, which leads to the lack of report on the evaluation of zTT for multilayers. The following paragraph explains this technical issue in detail.  Thin films, including multilayers, offer advantages for practical thermoelectric application, such as in micromachines and wearable devices, whereas the evaluation of their thermoelectric figure of merit is quite challenging. In the case of SE, thin films have garnered increasing attention because it has been demonstrated that the multilayer structure and high-density two-dimensional electron gas can improve the thermoelectric conversion performance of thin films in comparison to bulk materials [37]. It is essential for the SE to align the directions of charge and heat currents to prevent 4  an overestimation of the figure of merit. When a heat current is applied to the in-plane direction, the in-plane thermal conductivity is hard to be quantified because of heat leakage to the substrate. The quantitative evaluation of in-plane thermal conductivity has only been established in restricted structures, such as suspended or supported films [38]. On the other hand, when a heat current is directed perpendicular to the plane, evaluating the out-of-plane Seebeck coefficient poses challenges. Several recent reports have proposed a measurement method for the out-of-plane Seebeck coefficient, but this method does not account for the influence of contact/interfacial thermal resistances when measuring the temperature difference between the top and bottom surfaces of the thin-film sample [39,40]. In contrast to the SE, since the ANE allows the orthogonal configuration between the heat and charge currents, it is sufficient to evaluate ST and σyy in the in-plane direction and κxx in the out-of-plane direction. Various measurement methods, including optical and electrical techniques, have been well-established to quantify κxx of thin films in the out-of-plane direction [41–45], which is advantage of the ANE case. Nevertheless, no reports have been published to date on the zTT evaluation for thin film forms.  In this study, we propose and demonstrate the method accurately evaluating zTT in thin film forms. The values of ST, in-plane σyy, and out-of-plane κxx are investigated for the Fe/Pt metallic multilayers with the in-plane magnetized configuration. Samples were grown on two different substrates, which resulted in two different growth types: epitaxial and polycrystalline multilayers. These multilayers allow us to examine the effect of epitaxial growth on transport properties. To obtain out-of-plane κxx, the time-domain thermoreflectance (TDTR) method [42,43] was employed, which is a well-established technique for characterizing micro/nano-scale thermal transport, and is known for its ability to evaluate the effective out-of-plane κxx for metallic multilayers [46–48]. The value of ST for the in-plane magnetized configuration was measured by combining the heat flux method [49,50] and the κxx value from the TDTR measurement. The inherent structural anisotropy of multilayers leads to the difference in the electron transport properties between the in-plane and out-of-plane directions, which is evaluated as the ratio of electrical and thermal transport properties σyy/κxx. Finally, we systematically investigate the zTT value as a function of number of stacking repetitions N for the epitaxial and polycrystalline multilayers.   II. EXPERIMENTAL PROCEDURE Fe/Pt metallic multilayers were deposited on single-crystalline SrTiO3 (STO)(001) and amorphous quartz glass (hereinafter quartz for simplicity) substrates using an ultrahigh-vacuum-compatible magnetron sputtering system with a base pressure of approximately 10−7 Pa. The layer stackings from bottom to top were Fe(2 nm)/[Pt(tPt)/Fe(tFe)]N with N = 50, 100, and 200, where tPt and tFe are the unit thicknesses of Pt and Fe layers in the multilayer structure, respectively. Figure 2(a) illustrates the layer stacking of the multilayers. Prior to the sputter deposition, the STO substrate was 5  heated up to 450°C for surface cleaning while the quartz substrate was not heated. Then, all the Fe and Pt layers were deposited at room temperature. For the samples of TDTR measurement, the Al layer was deposited on the Fe/Pt multilayers at room temperature. On the other hand, the samples for measuring ST and σyy do not have an Al layer in order to prevent the electrical shunting problem. In addition to the Fe/Pt multilayers, the samples with the FePt alloy layers were prepared by co-deposition of Fe and Pt at room temperature as reference samples, in which the FePt was disordered because of the room temperature deposition without any thermal treatment and its composition is estimated to be Fe-rich from the equiatomic composition. Accurate determination of the Al thickness tAl, the total thickness of Fe/Pt multilayer tML, and the thickness of Fe-Pt alloy film talloy is essential because the TDTR measurements are exceedingly sensitive to these parameters. In order to determine these thicknesses, we performed cross-sectional scanning transmission electron microscopy (STEM) for the samples on STO. The structures of the Fe/Pt multilayers and FePt alloy films were characterized using x-ray diffraction (XRD).  The values of κxx, ST, and σyy were measured by employing the TDTR method, heat flux method, and conventional four-terminal method, respectively. Details of each method are as follows. TDTR is an optical pump-probe method that measures thermal transport properties by detecting the transient surface temperature modulation via thermoreflectance. The TDTR setup used in this study is based on front-heating and front-detection configuration, where the repetition rate, pulse duration, central wavelength, and 1/e2 spot diameter of pump (probe) laser were 20 MHz (20 MHz), 0.5 ps (0.5 ps), 1550 nm (775 nm), and approximately 90 μm (30 μm), respectively. The laser powers were determined so that the steady-state temperature rising at the sample surface was < 2 K [42]. Since the change in the surface reflectivity due to thermoreflectance is small (at most 0.01%), a lock-in detection scheme was conducted as following: the pump laser modulated at a frequency of 200 kHz was irradiated on the sample surface, the probe laser was focused on the same spot with a specific time delay which was electrically controlled by a function generator [10,51], and then the lock-in signals synchronized with the modulation frequency due to surface temperature response were characterized in the time domain by measuring the reflected probe laser using a balanced photoreceiver connected to a lock-in amplifier. The magnitudes of κxx were determined by a numerical simulation based on the one-dimensional heat diffusion model [52]. This approach was suitable because the spot diameter of pump laser significantly exceeded the heat diffusion length (approximately 2.5 μm) during the modulation period in the STO substrate, and consequently, heat can be regarded as flowing exclusively in the out-of-plane direction, thereby eliminating the need to consider in-plane heat conduction. In the heat diffusion model, the Fe/Pt multilayer was regarded as a single homogeneous layer, and thus the obtained κxx was the effective value for the multilayer, where the contributions of the Fe and Pt layers and Fe/Pt interfaces were included. For TDTR analysis, we used the lock-in phase value φTR, corresponding to the ratio of in-phase and out-of-phase components of lock-in signal, according to the 6  general analyses [42]. Note that the φTR data at the delay time of > 0.1 ns were used for analysis, where the electron-phonon coupling effect in the Al transducer layer dies out. ST for the in-plane magnetization configuration was evaluated using the heat flux method. It is known as a method with high reproducibility compared with the temperature difference method [50], which was demonstrated in the measurement of the SSE. This method gives the value of transverse electric field ET normalized by the applied heat flux −jq. Here, it is noted that ET is derived from the voltage measurement at an open circuit condition and the sign of ET is opposite to that of EANE [1]. ST can be quantitatively estimated using the relation of ST = κxxET/(−jq) derived from Eq. (1) and Fourier’s law. The details of the heat flux method are shown in the next section. An important point is that the κxx values can be obtained from the TDTR measurements as mentioned above. For the σyy, measurement, the standard four-terminal method was performed for the microfabricated devices. The samples were patterned into Hall bars through photolithography and Ar ion milling processes. The Cr/Au electrodes were fabricated using ion-beam sputtering and lift-off process. These measurements for transport properties were performed at room temperature and atmospheric pressure. In the heat flux method, the effects of heat loss due to radiation and convection were neglected.  III. RESULTS AND DISCUSSION Clear multilayer structures of the samples on STO are observed from the cross-sectional STEM images. Figure 2(b) shows bright field (BF)-STEM images for the Fe/Pt multilayers on STO with N = 50, 100, and 200. We experimentally obtain tAl and tML (talloy) for Fe/Pt multilayers (FePt alloy film) from BF-STEM images, which are summarized in Table 1. The high angle annular dark field (HAADF)-STEM images with higher resolution [see Fig. 2(c)] also confirmed that all of the Fe/Pt multilayer samples successfully form the layer stacking with clear interfaces. Figure 3 shows out-of-plane XRD patterns for (a) the Fe/Pt multilayers on STO and (b) quartz substrates. The XRD patterns for the FePt alloy films are also shown for comparison. All the Fe/Pt multilayers exhibit multiple peaks, and these diffraction patterns are reproduced by the calculation based on the Laue function with the assumption of the step model for the superstructure (see Supplemental Material [53]). From these XRD patterns and the reflection high-energy electron diffraction patterns (see Supplemental Material [53]), we found that the Fe/Pt multilayers and FePt layer on STO are epitaxially grown with the (100) preferential crystal orientation whereas those on quartz show the polycrystalline growth.  Figure 4(a)[4(b)] shows φTR for the Fe/Pt multilayers and the FePt alloy film on STO (quartz) substates as a function of the delay time between pump and probe lasers. The experimental data were well fitted by the one-dimensional heat diffusion model (black solid lines). The detailed information of TDTR analysis is described in Supplemental Material [53]. The estimated κxx values are summarized in Fig. 4(c). With increasing N of the multilayer film on both substrates, the κxx value 7  decreases. The difference in substrate, i.e., the difference in crystalline orientation and/or grain size does not noticeably affect the magnitude of κxx when comparing samples with the same N. Importantly, κxx of the Fe/Pt multilayers with N = 200 is apparently lower than that of FePt alloy films [shown as horizontal lines in Fig. 4(c)], proving that arrangement of multilayer structure effectively suppresses κxx for ANE-based thermoelectric devices. Figure 5(a) illustrates the setup to measure ST. A chip heater with a resistance of 1 kΩ and a size of 3.02×1.54×0.41 mm3, the sample with a size of about 5×2×0.5 mm3, and a sapphire slab with contact pads were stacked on a heat sink. The chip heater and sample were fixed with varnish, whereas the sapphire slab was fixed with a thermally conductive silicone adhesive sheet. The Al-1% Si bonding wires with a diameter of 25 μm (Cu wires with a diameter of 50 μm) were used for electrical connection between the chip heater (the sample) and contact pads to minimize the thermal conduction loss. The Cu wires were rigidly connected to the sample via indium soldering and the distance between the indium contacts was adjusted to the y-directional length of the chip heater l (= 3.02 mm). The measurement procedure is as follows; a heat flux jq was produced along the out-of-plane x direction through the sample by applying the power to the heater and the steady state of the system was achieved, then a magnetic field H was applied to the in-plane z direction, and a voltage Vy was measured along the in-plane y direction using a nanovoltmeter. A temperature rise ΔT of the heater surface from room temperature as a function of −jq was confirmed for the samples on STO and quartz substrates [Fig. 5(b)]. Here, the heater surface was covered with a black ink with emissivity of > 0.94, and ΔT was measured using an infrared camera. ΔT shows a linear response to −jq and the magnitude of ΔT reflects the difference in thermal conductivity of substrates. Figure 5(d) displays the H dependence of Vy for the Fe/Pt multilayer on STO with N = 200 for −jq = 48.4 kW m−2. The background contribution of induced electromotive force due to electromagnetic induction is subtracted in advance using a dataset for −jq = 0. It clearly exhibits the H-odd function in response to its magnetization reversal [Fig. 5(c)]. The value of ET is derived from the relation ET = (Vy+ − Vy−)/2l, where Vy+(−) is extrapolated from positive (negative) high magnetic field in the region of |H| = 6-10 kOe to zero magnetic field. Note that |H| = 6 kOe is much larger than the saturation magnetic field for all the samples. Figures 5(e) and 5(f) show the ET values as a function of −jq for the samples on STO and quartz, respectively. The ET/(−jq) values are evaluated from the slope of the linear fit, and ST was obtained using the experimentally obtained ET/(−jq) and κxx. Figure 6(a) shows the N dependence of ST for the Fe/Pt multilayers on STO and quartz. The ST values for FePt alloy films are shown as horizontal lines for comparison. ST increases monotonically with increasing N, and ST for the samples on STO tends to be larger than that for the samples on quartz. The FePt alloy film on quartz exhibits the maximum ST of (1.7±0.1) μV K−1, which is of the same order as the ANE coefficient of partially L10-ordered FePt alloy film for the out-of-plane magnetized configuration [54,55]. The enhancement of ST with increasing N is consistent with previous studies on 8  the ANE for multilayers [24,25]. Possible scenarios for explaining the enhancement of the ANE in this system are (i) the interdiffusion and alloying of Fe and Pt at the interfaces, (ii) the contribution of proximity-induced magnetic moments in Pt [24], and (iii) the enhancement of spin-orbit interaction at the interfaces. The well-defined structures of Fe/Pt multilayers shown in Fig. 2(c) suggest that there are few regions of intermixing between the Fe and Pt layers. Even if the ST in ultra-thin intermixed/alloyed layer is as large as that in the FePt alloy layer, the substantial ST enhancement cannot be attributed solely to the intermixing and alloying of Fe and Pt at the interfaces since the presence of shunting at remnant Pt layers would reduce the thermopower. Hence, scenario (i) does not account for the enhancement of ST. In addition, it has been demonstrated that the ANE for the Fe/nonmagnetic metal multilayers is enhanced regardless of the presence or absence of proximity ferromagnetism [24], which rules out scenario (ii) as the main contributing factor for the increase in ST with N for this system. At this moment, we believe that scenario (iii) plays a crucial role in achieving this enhancement. One may think that the SSE and SdSE could potentially contribute to enhancing ST in the Fe/Pt multilayer because both of them occur in a magnet/heavy metal junction in in-plane magnetized configuration. It should be emphasized that the SSE and SdSE cannot be experimentally separated from the ANE in the present measurement setup because they have the same thermoelectric symmetry as the ANE in the case of in-plane magnetized configuration. Moreover, the SSE can be enhanced by multilayer structure [56], whereas the SSE and SdSE are substantially affected by factors such as the thickness of Pt and Fe and the shunting effect to Fe layer. Therefore, it is difficult to quantitatively evaluate the contributions of the SSE and SdSE to the enhancement of ST. Nonetheless, it is quite possible that ST is enhanced by the contribution of the ANE alone. This is supported by the report that ST increases with increasing N in the Fe/Pt multilayers even for the out-of-plane magnetized configuration, in which the SSE and SdSE do not appear [24]. An interesting point is that the Fe/Pt multilayer with N = 200 on STO shows the value of ST nearly comparable to that of FePt alloy on STO. Each layer thickness for N = 200 is tFe ~ 0.5 nm and tPt ~ 0.7 nm, which is confirmed from Fig. 2(c). These thicknesses are still sufficiently larger than the unit cell size of FePt (~ 0.38 nm), and the local formation of FePt, for example at the interface, is not responsible for the value of ST. These facts mean that the origin of ST in Fe/Pt multilayers is a hybrid of several contributions, including the bulk ANE in Fe and Pt layers, interfacial ANE, SSE, and SdSE. These multiple origins are in contrast to the ST in the FePt alloy film, which originates solely from the bulk ANE in the FePt alloy layer. It is particularly interesting that despite the fundamentally different origins of the transverse thermoelectric conversion, the ST values for the Fe/Pt multilayer with N = 200 and FePt alloy film are comparable. In order to fully understand the connection between them, further investigation, including quantitative separation of the individual contributions within the Fe/Pt multilayer, is needed.  Subsequently, we investigate the N dependence of σyy for the Fe/Pt multilayers. Figure 6(b) 9  plots the N dependence of σyy for the Fe/Pt multilayers on STO and quartz. σyy is monotonically decreased with increasing N, and the minimum value is obtained at N = 200 for both substrates. Interestingly, while the σyy value for FePt alloy film shows minimum in the case of the sample on quartz, the σyy value for the FePt alloy film on STO is higher than that for the Fe/Pt multilayers on STO with N = 100 and 200. One possible explanation for this discrepancy is the reduced scattering of electrons due to relaxed lattice distortion in the epitaxial FePt alloy. While the dependence of σyy and κxx on N exhibits a similar decreasing behavior with increasing N, a discrepancy appears when the results are compared between the samples on STO and quartz substrates. To provide a detailed discussion of this discrepancy, the ratio of σyy to κxx, i.e., σyy/κxx as a function of N was plotted in Fig. 6(c). In both multilayers on STO and quartz, the σyy/κxx value reaches its maximum at N = 50 and subsequently diminishes to a nearly constant value at N = 100 and 200. This behavior is attributed to the influence of electron scattering at interfaces in the multilayer. Considering the anisotropic structure of multilayer, one may anticipate that the electrons moving in the out-of-plane direction are remarkably scattered at the interface, resulting in the anisotropy in electron transport between the in-plane and out-of-plane directions. As the thickness of each layer decreases, however, interfacial electron scattering affects electron transport in the in-plane direction as well as that along the out-of-plane direction, leading to less anisotropic behavior between the transport properties along the in-plane and the out-of-plane directions. The multilayers on STO exhibits larger σyy/κxx values than those on quartz, with the attenuation behavior being more pronounced in the former. This behavior is ascribed to the high crystalline orientation and/or large grain size of the epitaxial multilayers on STO in comparison to the polycrystalline multilayers on quartz. This allows interfacial electron scattering to exert a more prominent influence in the epitaxial multilayers, leading to boosting the anisotropy in the transport properties. Considering the expression for zTT, one can see that greater anisotropy between σyy and κxx, i.e., the higher σyy/κxx value, leads to a higher zTT. Therefore, to improve the transverse thermoelectric conversion performance by utilizing the structural anisotropy of the multilayer, it is essential to grow the multilayer epitaxially and optimize the thickness of each layer to maintain in-plane σyy. Finally, the zTT values for the Fe/Pt multilayers are evaluated using the obtained ST, σyy, and κxx values. Figure 6(d) shows the N dependence of zTT of the Fe/Pt multilayers at T = 296 K. The zTT value is increased with increasing N, and displays a consistently large value for the multilayers on STO compared to those on quartz. While the σyy/κxx value shows its maximum in the multilayer with N = 50 as shown in Fig. 6(c), the substantial contribution from ST achieves a maximum zTT value at N = 200. Considering that the epitaxial growth of multilayer hardly affects κxx and strongly affects the enhancement of ST and σyy, the epitaxial growth can be an effective strategy to increase the zTT of multilayers. It is worth mentioning that this study represents the pioneering effort in demonstrating the evaluation of zTT in thin film form. 10    IV. CONCLUSION  We demonstrated a measurement method for determining zTT value of thin films in the in-plane magnetized configuration. Utilizing our proposed methodology, we conducted a comprehensive investigation for the N dependence of ST, σyy, and κxx in the epitaxial and polycrystalline Fe/Pt metallic multilayers. The κxx value in the out-of-plane direction was measured using the TDTR method. ST for the in-plane magnetization configuration and σyy were evaluated using the heat flux method and conventional four-terminal method, respectively. The combination of the heat flux method and the TDTR method enabled us to evaluate the ST value for the in-plane magnetized configuration with high reproducibility, which could not be achieved using the conventional temperature difference method. The value of zTT increased with increasing N, which remarkably reflected the N dependent behavior of the ST values. ST and σyy were notably larger in the epitaxial multilayers than those for the polycrystalline multilayers, whereas negligible differences in κxx were observed between the epitaxial and polycrystalline multilayers. This difference between the epitaxial and polycrystalline multilayers was further confirmed in the σyy/κxx values, which reflected the degree of electron transport anisotropy. Taking into consideration the consistently larger ST and σyy/κxx values observed in epitaxial films, leading to enhanced zTT, it is suggested that epitaxial growth is a more efficient route than polycrystalline growth for ANE-based transverse thermoelectric conversion in multilayers. This study represents a pioneering effort in the evaluation of zTT in thin film form. Our proposed measurement technique unveils insights into the transverse thermoelectric properties inherent to multilayers and provides guidelines for designing multilayers that exhibit high transverse thermoelectric conversion performance: the balance of high anisotropy in transport properties (σyy/κxx) and large ST. We anticipate that this approach will greatly facilitate materials research in the field of thermoelectricity and spin caloritronics.   ACKNOWLEDGEMENTS The authors thank Y. Sakuraba for his help of supporting ANE measurements, M. Nagasako for his help of scanning transmission electron microscopy, and T. Sasaki, T. Endo, A. Nomura, and K. Harata for their help with the film deposition by ion beam sputtering. The device fabrication was partly carried out at the Cooperative Research and Development Center for Advanced Materials, Institute for Materials Research, Tohoku University. This work was supported by Grant-in-Aid for Scientific Research (S) (Grant No. JP18H05246 and JP22H04965) and Grant-in-Aid for Research Activity Start-up (Grant No. JP22K20495) from JSPS KAKENHI, Japan; CREST “Creation of Innovative Core Technologies for Nano-enabled Thermal Management” (Grant No. JPMJCR17I1) and ERATO “Magnetic Thermal Management Materials” (Grant No. JPMJER2201) from JST, Japan. T. Y. is supported by JSPS through a Research Fellowship for Young Scientists (Grant No. JP22KJ0210). 11   [1] K. Uchida, W. Zhou, and Y. Sakuraba, Transverse thermoelectric generation using magnetic materials, Appl. Phys. Lett. 118, 140504 (2021). [2] K. Uchida and J. P. 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B 92, 220407 (2015).   16  TABLE 1 Thickness values obtained by scanning transmission electron microscopy (STEM) images.   tML or talloy (nm) tAl (nm) Fe/Pt multilayer N = 50 209±3 47±6  N = 100 223±3 50±6  N = 200 232±2 48±4 FePt alloy film  216±2 48±3    FIG. 1 Schematic illustration of transverse thermoelectric conversion due to the anomalous Nernst effect (ANE) in a metallic multilayer. EANE, M, T, yy, and κxx denote the ANE-driven electric field, magnetization, temperature gradient, electrical conductivity, and thermal conductivity, respectively.    17    FIG. 2 (a) Layered structure of Fe/Pt metallic multilayers on SrTiO3 (STO)(001) and quartz substrates. (b) Cross-sectional BF-STEM images of Fe/Pt metallic multilayers on STO substrates for the overall sample cross section. (c) Cross-sectional HAADF-STEM images of Fe/Pt multilayers on STO substrates with higher resolution.    18   FIG. 3 Out-of-plane x-ray diffraction profiles for Fe/Pt metallic multilayers with N = 50, 100, and 200 and FePt alloy film on (a) STO and (b) quartz substrates. The asterisks in Fig. 3(a) denote the reflections from the STO substrates.  19   FIG. 4 (a),(b) TDTR phase data φTR vs delay time for Fe/Pt metallic multilayers with N = 50, 100, and 200 and FePt alloy film on (a) STO and (b) quartz substrates. Solid lines are the best fit curves based on one-dimensional heat diffusion model. (c) Number of stacking repetition N dependence of out-of-plane thermal conductivity κxx for Fe/Pt metallic multilayers on STO and quartz substrates. Solid (dashed) line shows the κxx value for FePt alloy film on the STO (quartz) substrate. Error bars represent the uncertainties considering the error propagation.  20   FIG. 5 (a) Schematic illustration of heat flux method. H and jq denote the magnetic field and heat flux, respectively. (b) Temperature rise of the heater surface ΔT as a function of applied heat flux −jq during the heat flux measurement. Error bars represent the standard deviations of the temperature data at the part of heater surface as captured by the infrared camera. (c), (d) Magnetic field H dependence of (c) magnetization M and (d) voltage along y direction Vy for Fe/Pt multilayer on the STO substrate with N = 200. The offset in (d) is due to the parasitic thermopower caused by the Seebeck effect at the electrodes for detecting Vy. The present measurement setup has several electrical contacts with different metals. In case that there is a slight temperature difference between the electrodes, the Seebeck effect at the electrodes appears as a H-independent thermopower. (e),(f) transverse electric field ET as a function of −jq for Fe/Pt multilayers and FePt alloy films on (e) STO and (f) quartz substrates. Solid lines represent the linear fitted lines. Error bars represent the uncertainties considering the error propagation.  21   FIG. 6 N dependence of (a) transverse thermoelectric coefficient ST, (b) electrical conductivity yy, (c) yy/κxx, and (d) figure of merit zTT for Fe/Pt metallic multilayers on STO and quartz substrates. Solid (dashed) lines represent the measurement results for FePt alloy films on the STO (quartz) substrate. Error bars in (a), (c), and (d) represent the uncertainty, where the error propagation is considered.   22  Supplemental Material for “Quantitative measurement of figure of merit for transverse thermoelectric conversion in Fe/Pt metallic multilayers” Takumi Yamazaki,1,*,§ Takamasa Hirai,2,†,§ Takashi Yagi,3 Yuichiro Yamashita,3 Ken-ichi Uchida,1,2  Takeshi Seki,1,2,‡ and Koki Takanashi4,5 1 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 2 National Institute for Materials Science, Tsukuba 305-0047, Japan 3 National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8563, Japan 4 Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan 5 Advanced Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan  * takumi.yamazaki.d5@tohoku.ac.jp † HIRAI.Takamasa@nims.go.jp ‡ takeshi.seki@tohoku.ac.jp § These authors contributed equally to this work.  S1. Reflection high-energy electron diffraction (RHEED) patterns for Fe/Pt multilayers  Figure S1 displays the typical reflection high-energy electron diffraction (RHEED) patterns for Fe/Pt multilayer on STO and quartz substrates with N =200. The diffraction patterns were observed just after the growth of the topmost Fe layer. For the Fe/Pt multilayer on the STO substrate, the period of spotty streaks varies with the azimuth relative to the electron beam direction, indicating that the Fe and Pt layers are epitaxially grown in the (001) plane. On the other hand, the multilayer on the quartz substrate exhibits broad spots and ring-shaped backgrounds, suggesting polycrystalline growth of Fe and Pt films.   S2. Step model for reproducing x-ray diffraction (XRD) pattern of Fe/Pt multilayer The step model is applicable to explain the peak positions for the experimental x-ray diffraction (XRD) profiles for the multilayers [1,2]. The x-ray scattering intensity 𝐼(𝑄) for the Fe/Pt multilayer is given by 𝐼(𝑄) = 𝐼𝑒|𝐹Fe(𝑄) + 𝐹Pt(𝑄)exp(𝑖𝑄𝑡Fe)|2 |∑ exp(𝑖𝑄𝑘Λ)𝑁−1𝑘=0|2, (S1) where 𝐼𝑒 is Thomson scattering intensity, 𝐹Fe(Pt)(𝑄) is the structural factor of Fe (Pt) layer, Λ is the multilayer period, and 𝑄  is the scattering vector. |∑ exp(𝑖𝑄𝑘Λ)𝑁−1𝑘=0 |2  corresponds to Laue function 𝐿(𝑄), and is expressed as 23  𝐿(𝑄) = |∑ exp(𝑖𝑄𝑘Λ)𝑁−1𝑘=0|2=sin2 (𝑁𝑄Λ2 )sin2 (𝑄Λ2 ), (S2) where N is the number of stacking repetition. The term of structural factor on the right-hand side of Eq. (S1) is expressed as |𝐹Fe(𝑄) + 𝐹Pt(𝑄)exp(𝑖𝑄𝑡Fe)|2 = |𝐹Fe(𝑄)|2 + |𝐹Pt(𝑄)|2 + 𝐹Fe(𝑄)𝐹Pt∗(𝑄)exp(−𝑖𝑄𝑡Fe) + 𝐹Fe∗(𝑄)𝐹Pt(𝑄)exp(𝑖𝑄𝑡Fe). (S3) Using the atomic scattering factor (𝑓Fe and 𝑓Pt), areal atomic density (𝜂Fe and 𝜂Pt), lattice spacing ( 𝑑Fe and 𝑑Pt ), and number of lattice plane ( 𝑛Fe and 𝑛Pt ), the term of structural factor can be transformed into  |𝐹Fe(𝑄) + 𝐹Pt(𝑄)exp(𝑖𝑄𝑡Fe)|2 = 𝑓Fe2(𝑄)𝜂Fe2sin2 (𝑛Fe𝑄𝑑Fe2 )sin2 (𝑄𝑑Fe2 )+ 𝑓Pt2(𝑄)𝜂Pt2sin2 (𝑛Pt𝑄𝑑Pt2 )sin2 (𝑄𝑑Pt2 ) +2𝑓Fe(𝑄)𝑓Pt(𝑄)𝜂Fe𝜂Ptsin (𝑛Fe𝑄𝑑Fe2 )sin (𝑄𝑑Fe2 )sin (𝑛Pt𝑄𝑑Pt2 )sin (𝑄𝑑Pt2 )cos (Λ𝑄2) . (S4) Figure S2 shows the comparison between the experimental XRD profile for N = 50 on STO and the calculated XRD profile. The experimental peak positions are reproduced by the calculation, indicating the well-defined structure of the present Fe/Pt multilayer.   S3. Details of time-domain thermoreflectance (TDTR) method  Our time-domain thermoreflectance (TDTR) measurement system with front-heating and front-detection configuration consisted of two lasers, and the delay time between the pump and probe lasers was electrically controlled [3,4]. The repetition rate, pulse duration, central wavelength, and 1/e2 spot diameter of pump (probe) laser were 20 MHz (20 MHz), 0.5 ps (0.5 ps), 1550 nm (775 nm), and approximately 90 μm (30 μm), respectively. The intensity of pump laser was modulated with a frequency of 200 kHz for lock-in detection.  Following to conventional TDTR experiments [5], some parameters were fixed besides the unknown thermal transport parameter of sample layer. In this study, the following parameters were the fixed values: volumetric heat capacity ρC (2.44×106 J m−3 K−1 [6]) and thermal diffusivity D (9.8×10−5 m2 s−1 [7]) of Al, ρC of Fe/Pt multilayer and FePt alloy film (3.13×106 J m−3 K−1), thermal effusivity of STO (4800 J m−2 s−0.5 K−1) and quartz (1450 J m−2 s−0.5 K−1), and thickness of Al, Fe/Pt multilayer, and FePt alloy film (see Table 1 in the main text). ρC of Fe/Pt multilayer and FePt alloy film was estimated by calculating the weighted average of the bulk ρC values of Fe and Pt [6], where ρ is density and C is specific heat. The thermal effusivity (= ρCD0.5) of STO and quartz substrates was verified by 24  individually measuring D using the laser flash method, C using the differential scanning calorimetry, and ρ using the Archimedes method by using plain STO and quartz substrates. The thickness of each layer was estimated from the STEM images. The out-of-plane thermal diffusivity Dxx of Fe/Pt multilayer and FePt alloy film, interfacial thermal resistance R1 between the Al layer and Fe/Pt multilayer or FePt alloy film (summarized in Fig. S3 as a function of N), and interfacial thermal resistance R2 (= 4.0×10−9 m2 K W−1) between Fe/Pt multilayer or FePt alloy film and substrates, were the fitting variables. From the obtained Dxx and given ρC of Fe/Pt multilayer and FePt alloy film, out-of-plane κxx (= ρCDxx) of Fe/Pt multilayer and FePt alloy film can be evaluated.  To ensure the validity of our TDTR method, we performed κxx measurements using pure-Fe films. Figure S4 shows the measured TDTR data and fitting curves for the 200-nm and 250-nm-thick Fe films on STO substrates. Faster decay of temporal response than that in Fe/Pt multilayers [see Fig. 5(a) in the main text] reflects much larger κxx of the Fe film. 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