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## Creator

Subrata Biswas, [Rajkumar Modak](https://orcid.org/0000-0001-7939-3289), [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), Ananthakrishnan Srinivasan, Perumal Alagarsamy, [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051)

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Subrata Biswas, Rajkumar Modak, Takamasa Hirai, Ananthakrishnan Srinivasan, Perumal Alagarsamy, Ken-ichi Uchida; Transverse magneto-thermoelectric properties of Fe2CoSi alloy and Fe2CoSi–Pt composite films. J. Appl. Phys. 14 April 2026; 139 (14): 145102 and may be found at https://doi.org/10.1063/5.0314309.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Transverse magneto-thermoelectric properties of Fe2CoSi alloy and Fe2CoSi–Pt composite films](https://mdr.nims.go.jp/datasets/b31e028a-7dcb-462f-9a37-fe7c8c5bbf02)

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Microsoft Word - Subrata_Manuscript_JAP25-AR-06640R - CORRECTIONPage 1 of 23 Transverse magneto-thermoelectric properties of Fe2CoSi alloy and Fe2CoSi-Pt composite films Subrata Biswas1,2,a), Rajkumar Modak1,3,a) , Takamasa Hirai1, Ananthakrishnan Srinivasan2, Perumal Alagarsamy2, and Ken-ichi Uchida1,3  1National Institute for Materials Science, Tsukuba 305-0047, Japan 2Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781-039, India 3Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan  a)subra176121021@iitg.ac.in (SB), rajkumarmodak24@gmail.com (RM)   ABSTRACT We report a systematic evaluation of the effects of post-deposition annealing temperature and structural ordering on the anomalous Nernst effect (ANE) in Fe2CoSi (FCS) Heusler alloy thin films. The study reveals that amorphous/disordered FCS films exhibit a larger anomalous Nernst coefficient (SANE) compared to their crystalline counterparts, in stark contrast to conventional Co-based Heusler alloys, which typically show maximum SANE in highly ordered structures. Furthermore, as a strategy for enhancing transverse thermoelectric properties, we explore (FCS)100−xPtx composite alloy films by systematically varying the Pt concentration and optimizing the composition. This method effectively enhances the transverse thermoelectric performance of the FCS-based alloys. Our findings offer valuable insights for the design and development of next-generation high-performance ANE materials.   Page 2 of 23 I. INTRODUCTION 1 Spin caloritronics is a multidisciplinary field that integrates principles from both spintronics 2 and thermoelectrics.1–3 This expanding area of investigation holds great promise for advancing 3 our understanding of fundamental phenomena at the intersection of spin-mediated electronic 4 and thermal transport effects.4–7 One fascinating phenomenon of this realm is the anomalous 5 Nernst effect (ANE), a transverse magneto-thermoelectric process wherein a charge current is 6 generated in directions perpendicular to temperature gradient (𝑇) and magnetization (M) of 7 magnetic conductors.4,8–11 ANE differs from the Seebeck effect, which generates the charge 8 current in a direction parallel to the temperature gradient. The orthogonal relationship in ANE 9 enables an increase in the thermoelectric output simply by enlarging the size of magnetic 10 materials, which can be exploited to design large-area, highly flexible, and versatile energy 11 harvesting and sensing devices.2,7,12–15 Despite these advantages, the lower thermopower of 12 ANE (i.e., the anomalous Nernst coefficient SANE) than that of the Seebeck effect (i.e., the 13 Seebeck coefficient SSE) is a serious impediment.1,2,16,17  14 To improve the performance of the transverse thermoelectric conversion based on ANE, 15 researchers have investigated transport properties in various magnetic materials.5,18–22 16 Ferromagnetic Heusler alloys with their unique electronic structure are promising candidates 17 for applications of ANE.6,20,23–26 In fact, Co-based Heusler alloys, such as Co2MnGa, 18 Co2MnAl1-xSix, have garnered considerable attention due to their large SANE, attributed to 19 substantial Berry curvature near the Fermi level.6,19,27 However, to achieve a highly ordered 20 crystal structure necessary for realizing large ANE in these Co-based Heusler alloys, the as-21 prepared alloys have to be annealed at high temperatures. In this regards, Reichlova et al. 22 reported a large ANE in Co2MnGa thin films grown and annealed at 500℃.19 Similarly, 23 Breidenbach et al. investigated the ANE in epitaxial Co2MnAlxSi1-x and Co2FeAl Heusler alloy 24 thin films grown on MgO seed layers, followed by annealing at 600°C to improve 25 crystallinity.25 Furthermore, Sakuraba et al. systematically studied the effect of atomic ordering 26 on the giant ANE in Co2MnAl1-xSix Heusler alloys by annealing the films between 500°C and 27 700°C.6 This process poses significant obstacle in the mass production of these Heusler alloys 28 for practical thermoelectric applications. Noky et al. carried out an extensive theoretical study 29 on the intrinsic anomalous transport properties of Heusler compounds, predicting that some 30 Fe-based Heusler alloys could exhibit significant ANE and anomalous Hall effect (AHE).28,29 31 Supporting these predictions, experimental results have shown that compounds such as 32 Fe2CoAl, Fe2CoGa, Fe2NiAl, and Fe2NiGa possess anomalous Hall conductivity values 33 Page 3 of 23 ranging from 250 to 750 S/cm. Despite these encouraging results, research on ANE in Fe-based 1 Heusler alloys remains limited, and their full potential for transverse magneto-thermoelectric 2 conversion is yet to be fully explored. 3 In addition to exploring new magnetic materials exhibiting large SANE, efforts to 4 enhance the performance of ANE have been made by fabricating an artificial magnetic 5 structure within existing material combinations.1,2,7,10,22,30–33 Alternating layers of 6 ferromagnetic (FM) and nonmagnetic (NM) thin films are an effective strategy to enhance SANE. 7 In this regard, Uchida et al. have demonstrated that FM/NM multilayers consisting of Fe/Pt, 8 Fe/Au, and Fe/Cu exhibit larger SANE than the single-layer Fe film and that the SANE value 9 increases when the interface density of the multilayers is increased.31 They have also reported 10 that the enhancement observed for Fe/Pt is higher than that of Fe/Au and Fe/Cu in the 11 multilayers with the same interface density, which may be attributed to the strong spin-orbit 12 coupling of the heavy metal (HM) Pt. Similar enhancements in SANE with the interface density 13 have been reported in Co/Pt multilayers33 and Ni/Pt superlattices.10 Interface-induced ANE 14 enhancement has also been observed in Fe3O4/Pt multilayers, where sub nanometer Fe-Pt 15 interdiffusion is believed to play a significant role.32 While previous studies focused on 16 increasing the FM/NM interfaces to improve ANE performance, the evaluation of FM-NM 17 composites that incorporate a heavy metal as the NM to enhance spin orbit interaction remains 18 limited. These composites, which possess the maximum number of interfaces and potentially 19 greater interdiffusion, remain largely unexplored.  20 In this study, we present a detailed investigation on the transverse magneto-21 thermoelectric properties of Fe2CoSi (FCS) Heusler alloy films aimed at evaluating the effects 22 of post-deposition annealing temperature and the subsequent improvement in structural 23 ordering on their transverse thermoelectric performance. To explore strategies for enhancing 24 this performance, we further examined (FCS)100−xPtx composite alloy films by systematically 25 varying the Pt concentration and optimizing the composition. For efficient optimization, we 26 employed a high-throughput material screening approach based on combinatorial materials 27 science and thermal imaging of the anomalous Ettingshausen effect (AEE), which is the 28 reciprocal of ANE, using lock-in thermography (LIT).4,8,13,14,30,34–38 Finally, uniform 29 (FCS)100−xPtx composite alloy films with the optimized composition were fabricated to evaluate 30 their transverse thermoelectric performance. This systematic study not only assesses the ANE 31 behavior of FCS Heusler alloys but also provides a valuable guideline for the future 32 development of high-performance ANE materials. 33 Page 4 of 23 II. EXPERIMENTAL DETAILS 1 A. Fabrication of uniform FCS and (FCS)100-xPtx composition gradient film 2 Uniform FCS films with a thickness of 50 nm were deposited on a single-crystalline MgO 3 (001) substrate at room temperature using a magnetron sputtering system. Prior to deposition, 4 the sputtering chamber was evacuated to a base pressure below 2×10-6 Pa, and the substrate 5 surfaces were treated in situ with low-power Ar-ion milling for 20 minutes to improve the 6 substrate interface. FCS thin films were then deposited at room temperature by co-sputtering 7 Fe, Co, and Si targets, using radio frequency (RF) power sources for Fe and Co and a direct 8 current (DC) power source for Si, at an Ar gas pressure of 0.6 Pa. Following deposition, in situ 9 post-deposition annealing was performed for 30 minutes under vacuum at three temperatures, 10 viz., Ta = 250 ℃, 350 ℃, and 450 ℃. To prevent oxidation, the as-deposited films were capped 11 with a 2 nm-thick Al layer before annealing. The elemental composition of all FCS films was 12 confirmed to be Fe:Co:Si ≈ 2:1:1 by X-ray fluorescence spectrometry. The as-deposited and 13 annealed FCS films of identical compositions were used for evaluation. 14  15 Fig. 1. (a) Schematic of the measurement configuration used for the anomalous Nernst effect 16 (ANE). 𝑇 is the temperature gradient and H is the magnetic field vector with the magnitude 17 of H. (b) The schematic of the Hall measurement configuration used to probe the anomalous 18 Page 5 of 23 Hall effect (AHE) under an out-of-plane magnetic field. Here, Jc is the charge current vector 1 applied along the length of the film. (c) Deposition protocol of (FCS)100-xPtx composition-2 spread film with wedge-shaped layer-by-layer deposition of FCS and Pt using a linearly 3 moving shutter. (d) Lithographically patterned configuration for the measurement of the 4 composition dependence of the anomalous Ettinghausen effect (AEE) in (FCS)100-xPtx films. 5 (e) Schematic of the AEE measurement system with different electrical components. 6 The (FCS)100-xPtx composition-gradient films with a thickness of 50 nm were fabricated 7 on a single-crystalline MgO (001) substrate. To achieve a composition variation of 0 ≤ x ≤ 100 8 at.% over a length of 7.0 mm on a single substrate, the films were prepared from Fe, Co, Si, 9 and Pt targets using a layer-by-layer wedge-shaped deposition process established in earlier 10 studies.20,30,39 The process involves three steps, viz., (i) deposition of a wedge-shaped FCS film 11 with a thickness gradient of 0.0–0.5 nm over a length of 7.0 mm using a linearly moving shutter, 12 (ii) rotation of the substrate by 180º, and (iii) deposition of a wedge-shaped Pt layer with the 13 thickness gradient of 0.0–0.5 nm over a length of 7.0 mm. The sequence (i) – (iii) forms a flat 14 (FCS)100-xPtx composition gradient film of thickness 0.5 nm. This sequence was repeated 100 15 times to get the 50 nm-thick (FCS)100-xPtx composition-gradient film [see Fig. 1(c)]. The 16 deposition condition for the FCS film in step (i) was kept identical to the condition used for 17 uniform FCS films discussed in experimental section A. A DC power source was used to 18 deposit Pt. The deposition was carried out at room temperature, and the as-deposited films were 19 capped with a 2 nm-thick Al layer. 20 B. Measurements of structural and transport properties for uniform films 21 The structural ordering in as-deposited and annealed FCS films was evaluated using X-22 ray diffraction (XRD) with a Cu Kα X-ray source (Rigaku Smartlab, λ = 0.15406 nm) in Bragg-23 Brentano geometry. For the measurements of AHE and ANE, the films were patterned into a 24 Hall bar structure with a width of 2.2 mm by photolithography, as depicted in Fig. 1(a, b).  For 25 the measurement of ANE, an out-of-plane magnetic field H and an in-plane 𝑇 were applied 26 to the film, and the H dependence of the transverse voltage V was recorded along the direction 27 perpendicular to both H and 𝑇 at different 𝑇 values. The value of 𝑇 was estimated by 28 recording a steady-state temperature profile of the films using an infrared camera, a technique 29 established in earlier studies.6,12,40,41 To ensure uniform emissivity, the surface of the FCS films 30 was coated with black ink before the temperature profile measurement.  31 Figure 1(b) schematically shows the configuration employed for Hall-effect 32 Page 6 of 23 measurements. The Hall resistivity 𝜌  was measured by applying a charge current of 100 μA 1 in the length direction of the Hall bar and sweeping H perpendicular to the film plane. The 2 electrical resistivity 𝜌  and Seebeck coefficient SSE of the films were measured using the 3 electrical resistance/Seebeck coefficient measurement system (ADVANCE RIKO, ZEM-3). 4 All the measurements were performed at room temperature (~300 K). 5 C. LIT measurement 6 For performing the AEE measurement using the LIT technique, the (FCS)100-xPtx 7 composition-gradient film was patterned into a device consisting of two (FCS)100-xPtx 8 composition-gradient rectangular wires with a width of 0.4 mm and a length of 8.0 mm, where 9 the composition gradient was along the length (x-direction) [see Fig. 1(d)]. During the LIT 10 measurement, the wires were electrically connected in series, with a charge current flowing in 11 opposite directions along the length. The magnetic field was applied along the width direction 12 of the wires (y-direction). In this condition, the temperature modulation is generated on the 13 sample surface due to the AEE-induced heat current along the thickness direction. The infrared 14 radiation thermally emitted from the sample surface was detected while applying a square-15 wave-modulated AC charge current with a square-wave amplitude of 25 mA, frequency f = 10 16 Hz, and zero DC offset along the wires and an external magnetic field μ0H of ± 0.5 T, where 17 μ0 is the vacuum permeability. To extract the pure AEE contribution from other thermoelectric 18 background signals, we employed the previously established procedures.20,30,36,37 Accordingly, 19 lock-in amplitude A and phase ϕ images showing the distribution of the current-induced 20 temperature modulation with the H-odd dependence were obtained by subtracting the raw LIT 21 images for M || +y from those for M || -y and dividing the subtracted images by 2. The 22 temperature modulation due to Joule heating was recorded by applying a square-wave-23 modulated AC charge current with the square-wave amplitude of 12.5 mA, frequency f = 10 24 Hz, and 12.5 mA DC offset in the absence of an external magnetic field. A schematic diagram 25 of the LIT measurement system is shown in Fig. 1(e). 26 III. RESULTS AND DISCUSSIONS 27 A. Dependence of transverse thermoelectric properties on structural ordering in single-28 layer FCS films 29 To investigate the relationship between structural stability, atomic disorder, and thermoelectric 30 Page 7 of 23 properties in FCS films, we fabricated 50-nm-thick FCS films at different post-deposition 1 annealing temperatures, Ta. XRD patterns of the as-deposited and annealed FCS films are 2 shown in Fig. 2(a, b). The as-deposited film exhibits no discernible XRD peaks, indicating its 3 amorphous nature. The presence of superlattice 002 and 004 peaks in the XRD pattern [see Fig. 4 2(a)] confirms evolution of crystalline ordering in annealed FCS films with a (001) preferred 5 growth direction. 6  7 Fig. 2. (a) XRD patterns (-2 scan, out-of-plane) of the as-deposited and annealed Fe2CoSi 8 (FCS) films. (b) -2  scan of the films oriented at   54.7 depicting (111) superlattice 9 reflection. Inset of (b) shows the 111 peaks for FCS thin films annealed at Ta = 350 °C and 10 450 °C, plotted with an enlarged intensity scale. (c) Unit cell of XA-type FCS alloy. (d) Unit 11 cell of disordered B2-type FCS alloy. (e) Estimated degree of XA- and B2-type ordering in the 12 as-deposited FCS film and the films annealed at different Ta, where the as-deposited FCS film 13 is shown at Ta = 0 ℃. 14 To quantitatively evaluate the evolution of crystalline ordering with Ta, we further 15 examined the XRD pattern in the (111) direction by tilting the sample stage by 54.7° from the 16 out-of-plane direction to record the 111 superlattice peak. As shown in Fig. 2(b), the 111 17 superlattice peak is absent in the XRD patterns of the as-deposited film and the film annealed 18 at Ta = 250 ℃. However, a weak 111 superlattice peak is observed for the film annealed at Ta 19 Page 8 of 23 = 350 °C (see inset of Fig. 2(b)), indicating the onset of chemical ordering. The 111 peak 1 becomes clearly pronounced for Ta = 450 °C, reflecting enhanced XA ordering with increasing 2 Ta. A faint fundamental 222 peak also appears for the Ta = 350 °C and Ta = 450 °C films. The 3 002 and 111 superlattice peaks provide information about the degree of atomic ordering in 4 Heusler alloys, which can be quantified using the following formula42, 5 𝐼𝐼 .𝑆𝐼𝐼 .;         𝐼𝐼 .𝑆2 𝑆2𝐼𝐼 . (1) where, 𝐼 , 𝐼 , and 𝐼 represent the integrated intensities of the 002, 004, and 111 peaks, 6 respectively, and SB2 and SXA represent the degrees of B2 and XA ordering, respectively. It is 7 worthy to note that the fully ordered FCS alloy is known to form an XA-type (space group 8 F43m) inverse Heusler alloy structure.43,44 The subscripts exp. and cal. represent the values 9 obtained from the experimental and simulated XRD patterns for an ideal XA structure [Fig. 10 2(c)], respectively. The B2 order represents the exchange of crystalline sites between Si and 11 Fe/Co atoms [Fig. 2(d)]. To calculate SB2 and SXA parameters using Eq. (1), we performed 12 powder XRD pattern simulations for a fully XA-ordered FCS alloy using the “visualization for 13 electronic and structural analysis” software. To compare the simulated powder XRD pattern 14 with the experimental out-of-plane XRD data for the epitaxial films, appropriate multiplicity 15 factors were used for the 002, 004, and 111 peaks. 16  17 Fig. 3. (a) H dependence of the transverse voltage V divided by the distance between the voltage 18 probe electrodes d (i.e., V/d) at various values of 𝑇 for the as-deposited FCS film. (b) 𝑇 19 dependence of the transverse electric field generated by ANE (i.e., EANE) of the as-deposited 20 film. (c) Extracted ANE coefficient, SANE, 𝑆 𝜌 𝛼  and 𝑆 𝜌 𝛼 . 𝛼  (𝛼 ) is the 21 longitudinal (transverse) component of the thermoelectric conductivity. 22 The obtained SB2 and SXA parameters are summarized in Fig. 2(e). The SB2 and SXA values for 23 the as-deposited film were observed to be zero, indicating an amorphous structure, and 24 Page 9 of 23 gradually increasing with increasing annealing temperature, indicating the formation of 1 ordered structures. These results suggest that a highly ordered XA-type structure can be 2 obtained from the as-deposited amorphous FCS film by annealing it at Ta ≥ 450 oC for 30 3 minutes. Further, the improvement in the crystalline order is reflected in the increase in Ms 4 values from 446 emu/cc in the as-deposited film to 1030 emu/cc in the 450℃ annealed film. 5 A detailed discussion of the magnetization data is provided in the supplementary material (see 6 Note S2).  7 Now, we focus on investigating the influence of structural ordering on the transverse 8 thermoelectric properties of the FCS films. To compare these properties, we determined the 9 anomalous Nernst coefficient (SANE) for the as-deposited and annealed FCS films. SANE was 10 determined by measuring the temperature gradient 𝑇-dependent ANE-induced electric field 11 EANE using the relationship:6 12 𝐄 𝑆 𝑇𝐌|𝐌| (2)  13 where M is the magnetization vector with a magnitude of M. Figure 3(a) shows the H 14 dependence of V/d with d being the distance between the voltage probe electrodes, recorded at 15 different 𝑇 values for the as-deposited film. To determine SANE, the field-odd component of 16 EANE was extracted for each 𝑇 value from the H dependence of V/d for all the films. We 17 estimated this component by finding the zero-field intercept of the linear fit to the V/d versus 18 H data in the saturation (High field) region for each 𝑇. The 𝑇 dependence of EANE of the 19 as-deposited film is shown in Fig. 3(b), from which the SANE was estimated from the slope of 20 the linear fit passing through the origin. The obtained SANE values for the as-deposited and 21 annealed FCS films using this procedure are presented in Fig. 3(c). These results reveal an 22 unconventional trend, viz., while large SANE is typically observed in highly ordered crystalline 23 Co-based Heusler alloys,6,21,24,45 the present FCS films exhibit the largest SANE value for the as-24 deposited amorphous film, which gradually decreases with increasing crystalline ordering. 25 Page 10 of 23  1 Fig. 4. (a) Seebeck coefficient SSE and electrical resistivity 𝜌  of the FCS films as a function 2 of Ta. (b) H dependence of the Hall resistivity 𝜌  for the films annealed at different Ta. (c) 3 Anomalous Hall resistivity 𝜌  and anomalous Hall angle (𝜃 ) as a function of Ta. (d) 4 Transverse thermoelectric conductivity 𝛼  with different Ta. (e) Power factor of ANE (PFANE) 5 as a function of Ta. 6 To understand the mechanism and investigate the factors responsible for this unusual 7 behavior observed in FCS films, we evaluated the different contributions to SANE,  following 8 previous reports.6,30 SANE is usually expressed as 9 𝑆  𝑆 𝑆  𝜌 𝛼  𝑆 𝜌 𝜌⁄  (3) Here, 𝜌 , 𝛼 , 𝑆 , and 𝜌  are the electrical resistivity, transverse thermoelectric 10 conductivity, Seebeck coefficient, and anomalous Hall resistivity, respectively. Although, in 11 general, Eq. (3) includes both ordinary and anomalous components, only the magnetization 12 dependent anomalous component is considered in this study. We measured 𝜌 , 𝑆 , and 𝜌  13 for the films to estimate the SI and SII contributions. 𝜌  and SSE of the films are shown in Fig. 14 4(a). The magnitude of SSE increases with increasing Ta, reaching 17.4 µV K-1 for the film 15 annealed at Ta = 450 ℃. The observed SSE value for XA-ordered FCS film is comparable with 16 those of other Fe-based ordered Heusler alloys, such as Fe2CoAl (SSE = 17.5 µVK-1), Fe2NiAl 17 (15 µVK-1), and Fe2NiGa (19.3 µVK-1).24,46 The 𝜌  value monotonically decreases with an 18 Page 11 of 23 increase in Ta, which is attributed to the improved crystalline order of the FCS films with 1 increasing Ta. The 𝜌  value of the FCS film annealed at Ta = 450 ℃ (0.71 µ m) is 2 comparable with the value reported previously in ordered FCS films.47 Figure 4(b) shows the 3 out-of-plane H dependence of 𝜌  for the as-deposited and annealed FCS films at various Ta 4 values. The 𝜌  values were then estimated from the H-odd dependence of the 𝜌  data at 5 saturation. Figure 4(c) displays the 𝜌  and anomalous Hall angle, 𝜃 𝜌 /𝜌 , values for 6 the as-deposited and annealed FCS films at various Ta values. Similar to SANE, both 𝜌  and 7 𝜃  are largest for the as-deposited amorphous/disordered FCS film and gradually decrease 8 in the films with increased crystalline ordering achieved due to annealed at higher Ta. From 9 these experimentally obtained values of SANE, SSE, 𝜌 , 𝜌 , we estimated SI and SII, which are 10 summarized in Fig. 3(c). The data reveal that, for both as-deposited and annealed FCS films, 11 SANE is dominated by the SI term, due to the combined effect of 𝜌  and 𝛼 . The data also 12 reveal that the large SANE in the as-deposited FCS film is due to a large 𝑆I compared to that for 13 the annealed films, which can be correlated with the larger 𝜌  for the amorphous/disordered 14 as-deposited FCS film compared to its ordered crystalline phase counterparts. It is worth 15 mentioning that no systematic Ta dependence is observed in the 𝑆I term of the annealed FCS 16 films. However, a gradual decrease in the 𝑆II term is observed with increasing Ta due to the 17 rapid decrease in 𝜃  despite the gradual increase in SSE (except for the as-deposited FCS 18 film, for which the very small SSE value results in the smallest 𝑆II despite the maximum 𝜃 ). 19 To further clarify the origin of the large 𝑆I term for the as-deposited FCS film, we further 20 evaluated 𝛼  using the relation 𝛼 𝑆 /𝜌 , and found that it is largest for the as-deposited 21 film. Here again, no systematic correlation is observed with Ta [see Fig. 4(d)]. However, the 22 detailed investigation of the different components in SANE clearly reveals that the large 𝜌  and 23 𝛼  are responsible for the large 𝑆I term for the as-deposited FCS film, with large 𝜌  being the 24 major contributor.  25 To evaluate the ANE performance of a material, not only is a large SANE value important, 26 but the evaluation of the power factor (PFANE), represented by 𝑆 /𝜌 , is also necessary. 27 Therefore, we evaluated PFANE for the FCS films and the results obtained are presented in Fig. 28 4(e). PFANE exhibits its maximum value for the as-deposited FCS film and gradually decreases 29 with increasing Ta, following the same trend observed in SANE. While the observed SANE and 30 PFANE values are lower than those reported for many conventional and XA-type ordered Fe-31 based Heusler alloy films,6,19,20,24 these results offer a new perspective that diverges from the 32 conventional approach of focusing on highly ordered Heusler alloys to achieve large ANE. 33 Page 12 of 23 This study indicates the unconventional behavior that amorphous/disordered Heusler alloys 1 exhibit larger ANE than their ordered crystalline counterparts. The amorphous nature of such 2 alloys is expected to offer advantages in fabrication and application flexibility. 3 B. Evaluation of FCS-Pt composite alloy films 4 To explore the possibility of further improving SANE of the as-deposited 5 amorphous/disordered FCS films, we evaluated FCS-Pt composite alloys. Since we observed 6 the maximum SANE for the as-deposited amorphous/disordered FCS film, we focused only on 7 FCS-Pt composite alloy films deposited at room temperature. To determine the optimum ratio 8 of FCS and Pt, we systematically varied Pt at.% from 0 to 100% and evaluated transverse 9 thermoelectric properties of the FCS100-xPtx composite alloy system. The systematic variation 10 of x by preparing many films involves time-consuming experiments and puts a large demand 11 on material and experimental resources. Further, the finite number of test films also limits the 12 determination of the best composition accurately. Therefore, for a better and efficient 13 optimization process, we adopted the previously established procedure of high throughput 14 evaluation of transverse thermoelectric materials utilizing the composition gradient films and 15 LIT technique based on active infrared imaging.14,20,30,36-38 A composition gradient film has a 16 continuous variation of x and eliminates the requirement of fabrication of several films, thus 17 reducing the time, material, and resource consumption. For this purpose, a composition 18 gradient FCS100-xPtx composite alloy film was deposited on a single-crystalline MgO(100) 19 substrate at room temperature (see the experimental section A for the detailed procedure of the 20 film fabrication). However, the direct measurement of ANE for such a composition-spread film 21 requires the preparation of many Hall bar-type structures to investigate the composition (x) 22 dependence of ANE. Since there is a limitation on the number of Hall bars made along the 23 composition gradient to reduce difficulty in ANE measurements, it limits the minimum 24 composition difference between two successive bars. Moreover, one-by-one thermopower 25 measurements take a long time. The LIT imaging detection enables high-throughput material 26 screening for ANE through the measurement of its Onsager reciprocal, viz., AEE. The AEE 27 measurement using LIT requires only a simple strip along the composition gradient as shown 28 in Fig. 1(d), thus enabling easy and efficient scanning for the best composition region in a 29 composition-spread film. Importantly, the AEE data is continuous along the composition 30 gradient, which gives a much accurate composition dependence of ANE/AEE. Therefore, to 31 efficiently evaluate the magneto-thermoelectric conversion property of the FCS100-xPtx 32 Page 13 of 23 composition-gradient film, AEE was measured along the composition gradient using the LIT 1 technique (see experimental section C for LIT measurement procedure).  2  3 Fig. 5. (a) Temperature-modulated AJoule and ϕJoule induced by Joule-heating (upper row) at f = 4 25 Hz, and Jc = 25 mA. AAEE and ϕAEE images generated (lower row) at f = 10 Hz, Jc = 25 mA, 5 and μ0H = 0.5 T along the film plane. Variations of (b) AJoule /jc2, and (c) AAEE/jc with Pt at.% 6 in the FCS100-xPtx composition-gradient film. 7 Figure 5(a) shows the A and 𝜙 images of the temperature modulation due to the Joule 8 heating (defined as AJoule and 𝜙Joule) and AEE (defined as AAEE and 𝜙AEE), respectively. The 9 AJoule value is proportional to the local resistivity in our configuration because the charge 10 current density jc is uniform and the heat loss from the film to the substrate is independent of 11 the position.20 Figure 5(b) presents the x dependence of AJoule/jc2 for the FCS100-xPtx 12 composition-gradient film extracted by averaging y-directional line profiles of the AJoule image 13 on the sample area represented by the rectangle box in Fig. 5(a). Variation of AJoule/j2c with x 14 shows a nearly linear decreasing trend with an increase in x (Pt at.%) content in the (FCS)100-15 xPtx composite film. This tendency is consistent with the fact that FCS has higher resistivity 16 than Pt and the Pt volume fraction increases with increasing x. Figure 5(c) displays the x 17 dependence of AAEE/jc for the (FCS)100-xPtx composition-gradient film extracted by averaging 18 y-directional line profiles of the AAEE image obtained by extracting the H-odd component of 19 the detected LIT images.14,20,30,37 The result readily shows that around x = 50 at.%, the 20 maximum AEE-induced temperature modulation can be observed revealing the optimum 21 Page 14 of 23 composition for best AEE performance to be (FCS)50Pt50 for the (FCS)100-xPtx composite alloy 1 system. While this high throughput screening of (FCS)100-xPtx composite alloys qualitatively 2 suggests the optimum composition for the FCS-Pt composite and a possible enhancement of 3 ANE signals based on the reciprocal relationship with AEE and ANE, the direct measurement 4 of ANE in these alloys is necessary to quantitatively evaluate the enhancement in transverse 5 thermoelectric performance of the alloy. 6  7 Fig. 6. (a) Extracted ANE coefficient, SANE, 𝑆  and 𝑆 , (b) power factor PFANE, (c) 𝜌  and SSE, 8 (d) 𝜌  and 𝛼  of as-deposited FCS (black) and (FCS)50Pt50 (red) thin film. 9 To quantitatively evaluate the transverse thermoelectric performance of the optimized 10 FCS-Pt composite system, we fabricated a uniform (FCS)50Pt50 film by ultra-thin [FCS (0.5 11 nm)/Pt (0.5 nm)]100 stacks, resembling the fabrication process of composition gradient film as 12 well as by co-sputtering. It has been previously reported that layer by layer deposition of ultra-13 thin layers induces atomic intermixing at the microstructural level, resulting in composite 14 formation.30 The measurement condition and the analysis process used to determine SANE are 15 identical to those described in the previous section. The observed SANE value for the uniform 16 (FCS)50Pt50 film is shown in Fig. 6(a) and compared with that of the as-deposited FCS film. As 17 can be seen from Fig. 6(a), nearly two times larger SANE is observed for the (FCS)50Pt50 18 composite alloy as compared to pure FCS. The observed SANE of  ~1.07 µV K−1 for the 19 (FCS)50Pt50 composite is comparable to those reported for various amorphous thin films30, and 20 Fe-based ordered Heusler alloys such as Fe2NiGa, Fe2NiAl, Fe2CoGa.24 The value of SANE 21 obtained for the (FCS)50Pt50 composite film is comparable to or higher than the values reported 22 Page 15 of 23 for well-established Fe/Pt and Co/Pt composite/multilayer systems, which typically exhibit 1 SANE values in the range of 0.56 μV K-1 to 1.2 μV K-1, depending on thickness, interface density, 2 and measurement geometry at room temperature.31,33,48 There is no significant difference in 3 SANE observed between the (FCS)50Pt50 fabricated by layer by layer deposition and co-4 sputtering. This result is consistent with previous reports which show that atomic mixing occurs 5 in ultrathin multilayer films and such systems behave as a single alloy composite.30 6 Furthermore, PFANE of the (FCS)50Pt50 composite films is ~7 times larger [see Fig. 6(b)] than 7 the as-deposited FCS alloy film owing to its significantly smaller 𝜌  [see Fig. 6(c)] due to Pt 8 doping, which has much lower resistivity. 9 To further understand the origin of the enhancement in SANE in the (FCS)50Pt50 10 composite film, the contributions of SI and SII to SANE have been evaluated using the 11 experimentally obtained values as shown in Fig. 6(a) and 6(c-d). The data reveal that the 12 enhancement in SANE in the (FCS)50Pt50 composite is due to the enhancement in the SI term, 13 and there is no significant variation in the 𝑆II term. To further clarify the origin of the large 𝑆I 14 term in the (FCS)50Pt50 film, 𝛼  was evaluated for the (FCS)50Pt50 composite film using the 15 relation 𝛼 𝑆 /𝜌  [see Fig. 6(d)]. The 𝛼  value was found to be more than two times 16 larger than that of the FCS alloy, clarifying its dominant contribution in the enhancement of 17 SANE for the (FCS)50Pt50 composite alloy film. While the microscopic origin of such behavior 18 requires a more detailed investigation in a future study, it can be speculated to have a similar 19 physical mechanism as discussed in previous studies of FM/HM films31–33, assuming that these 20 composite alloys have the maximum number of interfaces between FCS and Pt. 21 To distinguish interfacial effects in the FCS-Pt composite films, we investigated its 22 modulation in FCS/Pt multilayers. For this study, [FCS (tFCS)/Pt (0.5 nm)]n multilayer films 23 were prepared by repeating the FCS and Pt layers with the repetition number n. The Pt layer 24 thickness was fixed at 0.5 nm across all stacks, whereas different stacks were fabricated, each 25 with an FCS layer thickness (tFCS) fixed at 0.5, 1.0, 2.0, 5.0, and 10.0 nm. The n value for each 26 film was determined so that the total thickness of FCS layers in the multilayer was fixed at 50 27 nm (i.e., n = 50/tFCS). All the other fabrication conditions remained the same as discussed in 28 Section II.A. The uniform (FCS)50Pt50 composite film was compared with the ultra-thin [FCS 29 (0.5 nm)/Pt (0.5 nm)]100 multilayer stacks, considering the possibility of natural mixing in ultra-30 thin layers.30 To prevent oxidation, the (FCS)50Pt50 film was capped with a 2-nm-thick Al layer. 31 Since the maximum SANE was obtained in the as-deposited FCS film, only the as-deposited 32 Page 16 of 23 films were studied. The structural and transverse thermoelectric properties of the as-deposited 1 multilayer films and (FCS)50Pt50 film of uniform compositions were then evaluated and 2 compared to understand the origin of the enchantment of SANE in (FCS)50Pt50. 3 The detailed analysis of the experimental data of the [FCS (tFCS)/Pt (0.5 nm)]n 4 multilayer films is summarized in the supplementary material (see Note S1). The similarity in 5 XRD patterns (see Figure S1) between the FCS (0.5 nm)/Pt (0.5 nm) multilayer and the uniform 6 (FCS)50Pt50 film suggests the possibility of natural intermixing at the interfaces of such 7 ultrathin layers.30 This intermixing can result in a compositionally mixed region, making the 8 multilayer structure exhibit an XRD pattern similar to that of the uniform film. 9  10 Fig. 7. (a) Extracted values of SANE, SI and SII as a function of n, (b) 𝛼  versus n, and (c) PFANE 11 versus n plot. In all the graphs, the shaded data point represents the (FCS)50Pt50 uniform 12 composite film for comparison with the multilayer films. 13 Figure 7(a) summarizes the values of SANE, SI, and SII for the [FCS (tFCS)/Pt (0.5 nm)]n 14 multilayers alongside the (FCS)50Pt50 film. It is clearly observed that there is a sharp increase 15 in SANE for the n = 100 multilayer film, which is nearly the same for the uniform (FCS)50Pt50 16 Page 17 of 23 composite film. The result also shows that the major contribution to SANE comes from the SI 1 term, although SII increases with increasing n. To gain deeper insight into the origin of the large 2 𝑆I term, we further evaluated 𝛼  using the relation 𝛼 𝑆 /𝜌 , and observed a steady 3 increase with n, reaching its highest value the (FCS)50Pt50 film [see Fig. 7(b)]. This detailed 4 analysis of SANE components clearly demonstrates that the significant enhancement in 𝛼  is 5 primarily responsible for the large SI term in the multilayer films as well as in the (FCS)50Pt50 6 composite film. To assess the ANE performance of the multilayers, we also evaluate the PFANE. 7 Similar to 𝛼 , a huge increment (575 %) in PFANE can be obtained due to the concerted action 8 of the increase in SANE and significant decrease in 𝜌  with increase in n from [Fig. 7(c)]. 9 Notably, the PFANE value for the (FCS)50Pt50 film surpasses that of the n = 100 multilayer, 10 which is expected given its higher 𝛼  and lower 𝜌 . These experimental findings highlight 11 that multilayering with Pt and increasing interface density serve as effective strategies for 12 enhancing ANE performance in disordered FCS alloy films. 13 The observed enhancement may originate from several mechanisms, including 14 interfacial spin orbit coupling, proximity induced magnetism in Pt, and possible intermixing or 15 alloying at the FCS/Pt interfaces.10,31-33 As the number of bilayer repetitions n increases, 16 corresponding to a reduction in the FCS layer thickness and an increase in interface density, 17 SANE initially increases monotonically up to n < 25. This behavior is consistent with an 18 enhanced interfacial contribution to the ANE. However, for n = 25, a noticeable reduction in 19 SANE is observed, followed by a rapid increase for n = 100.10,31 At very high n values, the ultra-20 thin FCS layers may interdiffuse, forming an alloy of FCS and Pt. This intermixing may lead 21 to the formation of an effective FCS-Pt composite phase with enhanced spin orbit interaction 22 distributed throughout the film volume rather than being confined to discrete interfaces. 23 Consequently, the superior ANE performance observed in the FCS-Pt composite can be 24 attributed to enhanced spin orbit interaction and interfacial effects arising from intermixing 25 between FCS and Pt. This result demonstrates that FM-NM composite film using a heavy metal 26 as NM, such as Pt can provide an effective pathway for enhancing the transverse thermoelectric 27 performance of a magnetic material, including Heusler alloys. These outcomes provide 28 guidelines to develop new composite ANE materials with enhanced transverse thermoelectric 29 performance, which can potentially be realized in bulk or ribbon-type composite systems as 30 well. 31  32 Page 18 of 23 IV. CONCLUSION 1 In summary, we have systematically investigated the effect of post-deposition annealing 2 temperatures and the consequent evolution of crystalline ordering on the transverse magneto-3 thermoelectric conversion properties of FCS Heusler alloys. Our study finds that SANE in the 4 FCS films is relatively lower compared to traditional Heusler alloys, primarily due to the 5 significantly smaller 𝛼 . However, the study revealed that in contrast to conventional Heusler 6 alloys behavior, the as-deposited amorphous/disordered FCS film exhibits a larger SANE than 7 its crystalline counterparts, attributed to higher electrical resistivity 𝜌 , while 𝛼  remains 8 comparable. Furthermore, by forming composite alloys with heavy metal element Pt, both the 9 𝛼  and SANE could be nearly doubled in the FCS films. Notably, the power factor is enhanced 10 by nearly six times in the composite films. These findings demonstrate that, beyond traditional 11 FM/HM multilayer structures, FM-HM composites can also serve as an effective strategy for 12 enhancing the magneto-thermoelectric conversion performance of ferromagnetic materials, 13 including Heusler alloys. Thus, this study provides new guidelines for the design and 14 development of advanced ANE materials. 15 SUPPLEMENTARY MATERIAL  16 The supplementary material includes details on the transverse thermoelectric properties 17 of FCS/Pt multilayer films as a function of interface number (n) and the annealing temperature 18 dependence of magnetization in uniform FCS films. Figure S1 shows the multilayer schematics 19 and XRD patterns. Figure S2 presents the magnetic field dependence of V/d and ∇T dependence 20 of EANE. Figure S3 compares the thermoelectric performance of multilayer films with the 21 uniform (FCS)50Pt50 composite film. Figure S4 shows the isothermal magnetization curves of 22 as-deposited and annealed FCS films and their saturation magnetization compared with bulk 23 FCS. 24 ACKNOWLEDGEMENTS  25 The authors thank R. Nagasawa and V. Kushwaha for technical support and R. Iguchi and Y. 26 Sakuraba for valuable discussions. This work was partially supported by ERATO “Magnetic 27 Thermal Management Materials Project" (No. JPMJER2201) from JST, Japan; Grant-in-Aid 28 for Scientific Research (S) (No. 22H04965) from JSPS KAKENHI, Japan; and NEC 29 Corporation. SB was supported by the International Cooperative Graduate Program between 30 Page 19 of 23 the National Institute for Materials Science and the Indian Institute of Technology Guwahati. 1 RM was partially supported by JSPS through the “JSPS Postdoctoral Fellowship for Research 2 in Japan (Standard)” (P21064). 3 AUTHOR DECLARATIONS  4 Conflict of Interest 5 The authors have no conflicts to disclose.  6 Data availability statement  7 The data that support the findings of this study are available from the corresponding author 8 upon reasonable request. 9 References 10 1 J. Wang, Y. Lau, W. Zhou, T. Seki, Y. Sakuraba, T. Kubota, K. Ito, and K. Takanashi, “Strain‐11 induced large anomalous Nernst effect in polycrystalline Co2MnGa/AlN multilayers,” Adv. 12 Electron. Mater. 8, 2101380 (2022). 13 2 K. Uchida, and J.P. Heremans, “Thermoelectrics: From longitudinal to transverse,” Joule 6, 14 2240–2245 (2022). 15 3 K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. 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