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## Creator

[Koichi Oyanagi](https://orcid.org/0000-0001-8784-078X), [Hossein Sepehri-Amin](https://orcid.org/0000-0002-7856-7897), Kenta Takamori, [Terumasa Tadano](https://orcid.org/0000-0002-8132-2161), Takumi Imamura, Ren Nagasawa, [Krishnan Mahalingam](https://orcid.org/0000-0002-0075-3657), [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), [Fuyuki Ando](https://orcid.org/0009-0003-7789-8170), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550), [Satoru Kobayashi](https://orcid.org/0000-0002-3545-2977), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051)

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[Simultaneous achievement of large anomalous Nernst effect and reduced thermal conductivity in sintered polycrystalline topological Heusler ferromagnets](https://mdr.nims.go.jp/datasets/b934ebcf-4095-45c9-bde0-9d4cbb4e5147)

## Fulltext

1  Simultaneous achievement of large anomalous Nernst effect and reduced thermal 1 conductivity in sintered polycrystalline topological Heusler ferromagnets 2  3 Koichi Oyanagia,b,c,*, Hossein Sepehri-Aminb,*, Kenta Takamoria, Terumasa Tadanob, Takumi 4 Imamuraa,b,d, Ren Nagasawab,d, Krishnan Mahalingamb,1, Takamasa Hiraib, Fuyuki Andob, 5 Yuya Sakurabab,d, Satoru Kobayashia, and Ken-ichi Uchidab,d,e,* 6  7 a. Faculty of Science and Engineering, Iwate University, Morioka 020-8551, Japan. 8 b. National Institute for Materials Science, Tsukuba 305-0047, Japan. 9 c. Center for Sustainable Materials and Interfacial Science, Iwate University, Morioka 020-10 8550, Japan 11 d. Graduate School of Science and Technology, University of Tsukuba, Tsukuba 305-8573, 12 Japan. 13 e. Department of Advanced Materials Science, Graduate School of Frontier Sciences, The 14 University of Tokyo, Kashiwa 277-8561, Japan. 15  16 *Corresponding authors. 17 Email addresses: k.0yanagi444@gmail.com (K. Oyanagi), H.SEPEHRIAMIN@nims.go.jp (H. 18 Sepehri-Amin), UCHIDA.Kenichi@nims.go.jp (K. Uchida). 19 1 Prsent address: Sreenidhi University, Hyderabad, 501301, India.   20   2  Thermoelectric conversion based on the anomalous Nernst effect (ANE) is promising for 21 energy harvesting as its transverse geometry enables the design of large-scale thermoelectric 22 devices with simple structures. While topological ferromagnets, typically single crystals, 23 exhibit large ANE, achieving high conversion performance remains challenging because it also 24 requires high electric conductivity and low thermal conductivity. Here, we report enhanced 25 transverse thermoelectric conversion performance in polycrystalline topological ferromagnet 26 Co2MnGa (CMG) prepared by spark plasma sintering. Optimization of the sintering conditions 27 for CMG leads to the anomalous Nernst coefficient of 7.5 µV K-1 at room temperature, 28 comparable to the highest value reported for the single crystals, and simultaneously reduces its 29 thermal conductivity by 34% compared to that of the single crystals without affecting the 30 electric conductivity. Owing to the transport properties that overcome conventional trade-off 31 relations, our optimized CMG slab shows the record-high value of the dimensionless figure of 32 merit for ANE at room temperature. Detailed nano/microstructure characterizations and first-33 principles phonon calculations clarify the unconventional dependence of the transport 34 properties on the degree of crystalline ordering and morphology of crystal-domain boundaries. 35 The results reveal the potential of polycrystalline topological materials for transverse 36 thermoelectric applications and suggest alternative strategies to nanostructuring for enhancing 37 thermoelectric performance. 38 Keywords: Anomalous Nernst effect, Heusler alloy, Microstructure characterization, 39 Thermoelectric materials, First-principles phonon calculation.  40   3  1. Introduction 41 The anomalous Nernst effect (ANE) refers to the conversion of a longitudinal heat current 42 into a transverse electric field in a magnetic material with spontaneous magnetization. Because 43 of the transverse geometry of the thermoelectric conversion, ANE enables the construction of 44 thermoelectric devices with convenient scalability and easy fabrication [1-4]. The output 45 voltage of ANE increases simply by increasing a length of the device perpendicular to the 46 applied temperature gradient, realizing a large-scale and junction-less thermoelectric module, 47 which cannot be achieved by the Seebeck effect used in conventional thermoelectric modules. 48 However, low thermoelectric conversion performance of ANE prohibits practical applications 49 for thermoelectric devices. 50 Heusler alloys have been studied for several applications including spintronic devices 51 with high Curie temperatures and tunable half-metallicity [5], the conventional thermoelectric 52 devices with large Seebeck coefficients [6], and solid-state refrigeration with large 53 magnetocaloric effects and magneto shape memory alloys with giant magnetic-field-induced 54 strain effects [7]. Recently, magnetic Heusler alloys have been getting much attention for the 55 transverse thermoelectric applications requiring lager ANE. For instance, a ferromagnetic Weyl 56 semimetal Co2MnGa (CMG) with the L21 fully ordered Heusler structure, one of topological 57 magnets exhibiting large anomalous Nernst coefficient SANE due to non-trivial band structures 58 [8-36], shows the largest SANE value around room temperature [13,14,18,19,23]. However, ANE 59 in CMG has been measured mostly in single crystals [13,18,19] (SANE = 6.0 ~7.9 µV K-1) and 60 epitaxial thin films [14,23] (SANE ~ 6.2 µV K-1), which are not compatible to scalability and 61 mass production. 62 For applications, polycrystalline slabs with large SANE are promising to construct low-63 cost and large-scale devices based on ANE [37-42]. Owing to small anisotropy in the transport 64 properties along the crystal orientation [13] and robustness to the grain boundary scattering [38], 65 giant ANE has been reported not only in the polycrystalline films [29,34] but also in the 66 polycrystalline slabs made by using a spark plasma sintering (SPS) method [37,38,41]. SPS is 67 a versatile pressure-assisted sintering method in short time and low energy cost, and thus useful 68 for controlling the microstructure in polycrystalline thermoelectric materials to improve their 69 thermoelectric performance [43-45]. Furthermore, Ravi et al. demonstrated the remarkable 70 change of SANE in Fe-based alloys by microstructure engineering [46]. Therefore, the 71 comprehensive understanding of the transport properties and detailed microstructure is crucial 72 for the improvement of the performance of ANE in polycrystal materials for thermoelectric 73 applications based on ANE. 74   4  In this study, we prepared polycrystalline CMG slabs with various sintering conditions 75 using the SPS method and investigated their transport properties to optimize thermoelectric 76 conversion performance of ANE, which is often evaluated by the dimensionless figure of merit 77 [47-49]: 78  𝑧!"#𝑇 =$!"#$ %&𝑇,                                                                                               (1) 79 where σ is the electric conductivity and κ the thermal conductivity at absolute temperature T. 80 The CMG slab sintered at a high temperature and high pressure exhibits SANE ~ 7.5 µV K-1, 81 which is comparable to the best value in the single- and poly-crystalline CMG slabs at room 82 temperature. We also achieved the decrease of κ with maintaining sufficiently large σ and SANE, 83 resulting in a record-high value of zANET around room temperature among all the bulk magnetic 84 materials reported so far. We then performed detailed nano/microstructure analysis on the 85 samples to clarify the influence of the nano/microstructure on the transport properties. 86 Transmission electron microscopy (TEM) results revealed the importance of the crystal growth 87 of the L21 ordered phase within the samples for showing large SANE even if its existence cannot 88 be detected by the X-ray diffraction (XRD). In addition to the conventional L21 and B2 phases 89 in CMG, we found an unknown crystal phase with a size of ten nanometers. This length scale 90 coincides with the scale of mean free paths for phonons which mainly contribute to the thermal 91 conductivity obtained by a first-principles calculation, suggesting that the nanometer-scale 92 crystal boundaries increase the phonon scattering and cause small κ. Our results provide an 93 insight into the correlation between the transport properties and nano/microstructures within 94 the sample, which is important for the simultaneous optimization of ANE, electric conductivity, 95 and thermal conductivity.  96 2. Experimental  97 The polycrystalline CMG slabs were prepared under various sintering conditions from 98 powder of CMG ingots. The detailed recipe for the preparation of CMG ingots is described in 99 Supplementary Information and Ref. 37. We crushed the CMG ingots using a mortar and 100 planetary ball mill, followed by sieving the ball-milled CMG powder through a 63 µm mesh. 101 An inductively coupled plasma optical emission spectrometer determined the composition of 102 the CMG powder to be Co52.1Mn23.1Ga24.8. We loaded the CMG powder into a graphite die with 103 a diameter of 10 mm and sintered it under various conditions. We examined nine sintering 104 conditions combining three sintering temperatures of Tsinter = 600, 700, and 800℃ with three 105 maximum sintering pressures of pmax = 30, 60, and 90 MPa. We kept Tsinter and pmax for 10 min 106 in all the conditions. In the following, we define the sample name as CMG(Tsinter, pmax) for each 107 sintering condition. The sintered CMG slabs were cut into a rectangular shape with a length of 108   5  9-10 mm, width of 2 mm, and thickness of 0.4-0.9 mm for measuring the transport properties 109 and magnetization M, and into a disc with a diameter of 10 mm and thickness of 1 mm for 110 measuring the thermal diffusivity, using a diamond wire saw. Note that the variation in the 111 shape of the rectangular samples does not affect the measurement results. 112 We measured ANE at room temperature and atmospheric pressure using a homemade 113 sample holder (Fig. 1a). The sample holder consists of two anodized Al plates. The large one 114 works as a thermal bath. The small one is equipped with a chip heater and is attached to the 115 large one but thermally isolated from it by inserting a Bakelite board to create a temperature 116 difference between the two plates. A sample was bridged between the plates and fixed with a 117 high-thermal conductivity adhesive sheet. A uniform temperature difference along the x 118 direction was generated using the chip heater. Because of the thermal resistance between the 119 sample and plates due to the presence of adhesive sheets, the temperature differences between 120 the ends of the sample and between the plates are different [50]. To accurately determine SANE, 121 we estimated the actual value of the temperature gradient in the x direction ∇xT directly from a 122 temperature-profile image at the surface of the sample coated with black ink using an infrared 123 camera. We measured the thermoelectric voltage along the y direction Vy, i.e., the sample width 124 direction, with the magnetic field H along the out-of-plane direction and converted Vy into the 125 transverse electric field Ey = Vy/w = SANE∇xT, where w is the sample width. The anomalous Hall 126 effect was measured in the same setup for the ANE measurement, where a charge current was 127 applied instead of the thermal gradient. The Seebeck coefficient and longitudinal electric 128 conductivity were measured using a Seebeck Coefficient/Electric Resistance Measurement 129 System (ZEM-3, Advance Riko, Inc.), which is similar to the system used in Ref. 51. The 130 sample is clamped by two metallic blocks and is attached by two R-type (PtRh-Pt) 131 thermocouple probes with the distance of 6 mm in a furnace under a He atmosphere. To measure 132 the Seebeck coefficient, a temperature gradient is applied to the sample by heating one metallic 133 block, and the resultant temperature difference and thermoelectric voltage at the same positions 134 were measured simultaneously using the probes. By applying a charge current to the sample 135 through the metallic blocks and measuring the voltage between the probes, we performed the 136 standard direct current four-terminal method for measuring the longitudinal electric 137 conductivity. The longitudinal resistivity of our samples is in the range from 1 µΩ m to 4 µΩ 138 m (see Fig. S1a). The thermal conductivity was estimated by multiplying the thermal diffusivity, 139 specific heat, and density. The disc shaped samples coated with black ink were used for the 140 laser flash method (LFA1000, Linseis Messgeraete GmbH) to measure the thermal diffusivity. 141   6  The specific heat and density were measured using differential scanning calorimetry (DSCvesta, 142 Rigaku Holdings Corp.) and Archimedes method, respectively. Note that the measurement 143 results are not affected by the direction in which the transport properties were measured on the 144 sample because of the homogeneity of the polycrystal slab [38]. The magnetization as a function 145 of temperature was measured in the range from 300 K to 850 K using a superconducting 146 quantum interference device equipped with a vibrating sample magnetometer (SQUID-VSM, 147 Quantum Design) and from 5 K to 350 K using a superconducting quantum interference device 148 (SQUID) magnetometer (MPMS-5L, Quantum Design), respectively. Scanning electron 149 microscopy (SEM) was performed using a Carl Zeiss CrossBeam 1540EsB microscope 150 equipped with an energy-dispersive spectroscopy (EDS) detector. Scanning transmission 151 electron microscopy (STEM) was conducted using a Titan G2 80-200 (FEI) with a probe 152 aberration corrector. The lift-out method was used to prepare the TEM specimens using a 153 focused ion beam system Helios G4-UX DualBeam (FEI). The surfaces of the samples were 154 observed using an ultra-low voltage SEM JSM-7800F Prime (Jeol Ltd.). 155 3. Results and discussion 156 Figure 1b shows the H dependence of Ey for CMG(800, 60) at different ∇xT values. Clear 157 Ey signals appear by applying ∇xT and H. The magnitude of the Ey signal increases by increasing 158 ∇xT and its sign reverses with respect to the sign of H. By increasing |H|, the Ey signal is 159 saturated at around |µ0H| ~ 0.8 T, which is consistent with the saturation field of M (see the 160 inset to Fig. 1b), indicating that ANE mainly generates the Ey signal. In this setup, an H-linear 161 signal due to the ordinary Nernst effect also appears. We subtracted the ordinary Nernst 162 component by linear extrapolation for the results above the saturation field, represented as the 163 colored dashed lines in Fig. 1b, and obtained the ANE component EANE at H = 0 (see the colored 164 dots). We estimated SANE = EANE/∇xT to be ~7.5 µV K-1 for CMG(800, 60) by a linear fit to the 165 ∇xT dependence of EANE in Fig. 1c. We obtained SANE for all the samples through the same 166 procedure. 167 We show the H dependence of Ey for CMG(600, pmax), CMG(700, pmax), and CMG(800, 168 pmax) in Figs. 2a, 2b, and 2c, respectively. We found clear anomalous Nernst signals appear in 169 all the samples and summarized their estimated SANE values in the left panel of Fig. 2d at room 170 temperature. SANE monotonically increases by increasing Tsinter, and the relationship of SANE at 171 the same Tsinter value is CMG(Tsinter, 30) < CMG(Tsinter, 60) ~ CMG(Tsinter, 90). All the samples 172 show relatively large SANE (> 2 µV K-1), and the maximum SANE value of 7.5 µV K-1 in 173 CMG(800, 60) is the largest among all the values previously reported in polycrystalline magnets 174   7  29,30,32,34,36-38,46,48,49,52-54] including topological materials. More importantly, the 175 maximum SANE value in the polycrystalline CMG slab is comparable to or even larger than that 176 in the single-crystalline CMG slabs [13,18,19] (see the blue and red dashed lines in the left 177 panel of Fig. 2d). 178 To further investigate large ANE in the polycrystalline CMG slabs, we estimated the 179 anomalous Nernst conductivity αxy. The left panel of Fig. 2e shows the obtained αxy values in 180 all the samples using the formula SANE = ρxxαxy - (ρAHESSE/ρxx) with the measured longitudinal 181 resistance ρxx, anomalous Hall resistivity ρAHE, and Seebeck coefficient SSE (see Fig. S1). αxy 182 depends on the sintering condition and its trend is similar to that of SANE, while both SANE and 183 αxy are independent of the saturation magnetization Ms (see the right panels in Figs. 2d and 2e). 184 The maximum value of ~ 3 A m-1 K-1 is comparable to that in the single-crystalline CMG 185 samples [13,18,19]. This indicates the crucial role of the Berry curvature and electronic band 186 structure at the Fermi level even in the polycrystals in showing large SANE, consistent with the 187 recent findings [29,30,32-38,40,41]. 188 We next focus on zANET to discuss the transverse thermoelectric performance of the 189 polycrystalline CMG slabs. σ and κ, which is obtained using the density, specific heat, and 190 thermal diffusivity (see Fig. S2), for all the samples are summarized in Figs. 3a and 3b. We 191 found that σ and κ of the samples prepared at Tsinter = 700℃ and 800℃ are larger than those of 192 the sample prepared at Tsinter = 600℃. Although σ of the samples prepared at Tsinter = 700℃ and 193 800℃ is comparable to that of the single-crystalline CMG samples, κ is maximally ~34% 194 smaller than that of the single crystal [19]. This indicates that we successfully reduced κ without 195 decrease of σ and SANE, which is important for improving zANET (see Eq. 1). Fig. 3c shows the 196 sintering condition dependence of zANET for all the samples, which is estimated from the results 197 in Figs. 2d, 3a, and 3b. The overall trend is determined primarily by SANE. The CMG(800, 60) 198 sample shows the maximum value of ~ 8.0 × 10-4, which is surprisingly greater than that for the 199 single-crystalline CMG slab (zANET ~ 2.0 × 10-4 in Ref. 13 and ~ 6.6 × 10-4 in Ref. 19 shown as 200 the red and blue dashed lines, respectively). Furthermore, this value is much larger than zANET 201 in other magnetic materials [12,13,18,19,21,27,46,48,49,52-54] exhibiting large ANE, such as 202 the single-crystalline Fe3Ga slab [21] and the polycrystalline SmCo5-type permanent magnets 203 [48], summarized in Fig. 3d. 204 Now, we consider the origin of the high-performance of ANE in the sintered CMG slabs. 205 We found that the samples sintered at Tsinter = 600℃ and 700℃ have a lower relative density, 206 the ratio of the measured density to the theoretical density, than that of the samples sintered at 207 800℃ (see Fig. S2) and a rough surface with remaining pores and microparticles (characterized 208   8  by ultra-low voltage SEM as shown in Fig. S3). These indicate that the samples sintered at 209 lower Tsinter are insufficiently densified, resulting in small SANE in CMG(600, pmax) and 210 CMG(700, 30). In fact, the CMG ingot annealed at 600℃ with the relative density nearly of 211 100% exhibits SANE of 5.4 µV K-1, which is much larger than that of the insufficiently densified 212 CMG(600, pmax) (SANE = 2 ~ 4 µV K-1), suggesting the correlation between SANE and the relative 213 density, rather than the exposed temperature. On the other hand, although both CMG(800, 30) 214 and CMG(800, 90) show the relative density of nearly 100% and dense morphology, CMG(800, 215 90) shows larger SANE than CMG(800, 30), indicating that the difference in the sample density 216 cannot explain large ANE in CMG(800, 90). Therefore, to understand the origin of large SANE 217 in CMG(800, 90), we performed the micro- and nano-scale structure analysis, i.e., SEM, energy 218 dispersive X-ray spectrometry (EDS), and high-resolution high-angle annular dark field 219 (HAADF) scanning transmission electron microscopy (STEM), on two samples.  220 Figures 4a and 4b show the SEM-EDS maps of Co, Mn, and Ga for the CMG(800, 90) 221 and CMG(800, 30) slabs. We found an inhomogeneous distribution of Mn in both samples 222 where Mn segregation can be seen at the surface of particles close to the grain boundary region. 223 In both samples, the typical grain size is comparable (a few to several tens of micrometers). 224 This grain size is consistent with the size of the initial powder of CMG, which was sieved 225 through a 63 µm mesh. 226 Figures 5a, 5b, and 5c show high resolution HAADF-STEM images and nano-beam 227 electron diffraction patterns obtained from CMG(800, 90) and CMG(800, 30). Although the 228 bulk XRD patterns show only fundamental diffraction peaks of the A2 phase (see Fig. S4), the 229 nano-beam diffraction patterns in the i and ii regions in Fig. 5a indicate the presence of the L21 230 and B2 ordered phases by 111 and 002 superlattice reflections in the diffraction patterns 231 obtained along [111] zone axis of matrix phase, respectively, indicating that the ordered 232 structure of CMG(800, 90) varies in the nanoscale containing. We found that the electron beam 233 diffraction pattern in the iii region is different from that of both L21 and B2 phases; an additional 234 superlattice reflection appears diagonally on either side of the 002 spot indicated by the white 235 allows in the bottom of the right panels of Fig. 5a. To closely see the crystal structure of this 236 unconventional modulated phase, we show the magnified HAADF-STEM images for the L21, 237 B2, and modulated phases in Fig. 5c. In comparison with the L21 and B2 structures, the 238 modulated phase consists of the relatively displaced atoms in the diagonal direction (see red 239 colored dots indicated by the white arrows in the right panel of Fig. 5c), similar to a martensite. 240 Although the TEM observation gives the local information, CMG(800, 30) seems to have a 241 larger amount of the modulated phase than CMG(800, 90) (see the lines of the displaced atoms 242   9  indicated by the white arrows in Fig. 5b), suggesting that the increase of the sintering pressure 243 at high sintering temperature facilitates the transformation of the modulated phase into the L21 244 and/or B2 phases. 245 We also found clear difference between CMG(800, 30) and CMG(800, 90) in the M-T 246 curves shown in Fig. 6. A large thermal hysteresis appears in CMG(800, 30) within the T range 247 from 500 K to 750 K, while it almost disappears in CMG(800, 90). The observed thermal 248 hysteresis is irrelevant to the magnetic ordering transition because M appears at around 800 K. 249 The onset temperature of M for CMG(800, 90) is lower than CMG(800, 30), and CMG(800, 250 30) shows larger M than CMG(800, 90). A similar thermal hysteresis has been observed in the 251 thin film of CMG [55] and other Heusler alloys with the martensitic transformations caused by 252 the distortion of the crystal structure [56-58]. In our case, the observed martensitic-253 transformation-like hysteresis can be caused by the diagonal displacement of the atoms in the 254 modulated phase (see Fig. 5c). Although determination of the actual Curie temperature is 255 difficult in our case due to the application of the large magnetic field, the onset temperature of 256 M at 1 T for CMG(800, 90) is closer to the literature Curie temperature for L21-type CMG [59] 257 (~685 K) than that for CMG(800, 30). By measuring the M-T curves at 1 T at low temperatures 258 (see the inset to Fig. 6), we obtained Ms at T = 5 K for CMG(800, 30) as 4.2 µB f.u.-1 and 259 CMG(800, 90) as 4.1 µB f.u.-1 CMG(800, 90) shows Ms consistent with the experimental and 260 theoretical values for L21-type CMG [59,60] (~4.1 µB f.u.-1) and closer to the experimental 261 value for the B2-type CMG film [61] at 4.2 K (~3 µB f.u.-1) than that for CMG(800, 30). All the 262 results indicate that the magnetic properties of CMG(800, 90) are more similar to those of 263 L21/B2-type CMG than those of CMG(800, 30), suggesting the transformation from the 264 modulated phase into the L21 and/or B2 phases. This interpretation is consistent with the TEM 265 observation. Therefore, the sintering pressure at high sintering temperature affects the degree 266 of the crystalline orders in the samples.  267 The above results confirm that the degree of the crystalline order is important for 268 obtaining large SANE [21,62,63]. We found that CMG(800, 90) exhibits the larger value of SANE 269 than that in CMG(800, 30), which has more modulated phase than the L21 and/or B2 phases. 270 Because the theoretical origin of large ANE in CMG is the topological electronic band structure 271 in the fully ordered L21 phase [13,18,62], our results suggest that ANE in the modulated phase 272 seems to be small, and thus the reduction of the modulated phase is crucial for obtaining large 273 SANE. 274   10  Now, we focus on the reduction of κ in CMG(800, 30) and CMG(800, 90). The inset to 275 Fig. 3b shows the sintering condition dependence of the nonelectronic thermal conductivity Δκ 276 = κ - κel, where the electronic thermal conductivity κel is estimated via the Wiedemann-Franz 277 law with the free-electron Lorenz number of 2.44 × 10-8 W Ω K-2. Since the values of σ in 278 CMG(800, 30) and CMG(800, 90) are comparable to that in the single crystal [19] (see Fig. 3a), 279 κel does not contribute to the decrease of κ in our samples. On the other hand, we found the 280 sizable decrease in Δκ compared with the single crystal's value (represented as the dotted lines). 281 Phonon and magnon can contribute to Δκ in magnetic materials [64]. However, we assumed 282 the magnon contribution is negligibly small in CMG at room temperature because the 283 experimental observation of magnon contribution has been typically at very low temperatures 284 [65,66] and the magnetic damping constant of the polycrystalline CMG [67] is one order of 285 magnitude larger than that of CoFe alloys which show measurable magnon contribution at room 286 temperature [68]. Therefore, the thermal conductivity carried by phonons plays an important 287 role in the decrease of κ. 288 A plausible mechanism of the decrease of Δκ is the increase of phonon-boundary 289 scattering caused by nano/microstructure [46-48]. To investigate the phonon thermal 290 conductivity κph, we carried out a first-principles calculation, whose details are described in 291 Supplementary Information, with taking 3- and 4-phonon, and isotope scatterings into account 292 and obtained cumulative κph, which provides a useful insight into the reduction of κph by 293 nano/microstructures. Fig. 7a shows cumulative κph as a function of the phonon mean free path 294 L for CMG at room temperature. Cumulative κph rapidly increases from L ~ 10 nm and is 295 saturated to ~ 23 W K-1 m-1 above L > 1 µm. The saturation value is comparable to the value of 296 κ in the single crystal and much larger than that in our samples. Our calculation indicates that 297 phonons with L in the range from 10 nm to 100 nm mainly carry heat in CMG, and scattering 298 centers with the size of such the scale can efficiently reduce κph. However, this length scale is 299 much smaller than the typical grain size with the order of 10 µm in both CMG(800, 30) and 300 CMG(800, 90) shown in the SEM images in Fig. 7b (showing the SEM images for all the 301 samples in Fig. S3). We ignored phonon-electron and phonon-magnon scatterings in the 302 calculation. They increase the phonon scattering and play an important role for quantitative 303 discussion on κ, but only make the length scale of the heat-carrying phonons shorter. Therefore, 304 even when phonon-electron and phonon-magnon scatterings are taken into account, the grains 305 of the order of 10 µm in size cannot be responsible for the decrease in Δκ due to the phonon-306 boundary scatterings. On the other hand, recall that the CMG samples contain the crystal phase 307 separation in the nanometer scale, as observed in Figs. 5a-c. The coincidence between L of the 308   11  heat-carrying phonons and the size of the crystal phase separation indicates that the crystal-309 domain boundary induces phonon scatterings, resulting in the decrease of Δκ. Our results 310 suggest that phonon engineering using not only grain boundaries but also crystal-domain 311 boundaries can increase the performance of thermoelectric materials. 312 4. Conclusion 313 In summary, we investigated ANE at room temperature in polycrystalline CMG slabs 314 prepared by the SPS method in various sintering conditions. The maximum values of SANE and 315 αxy of our polycrystalline CMG slabs prepared at a high sintering temperature and pressure are 316 comparable to those in the single-crystalline CMG slab and are largest at room temperature 317 among polycrystalline magnetic materials. Furthermore, the optimized CMG slab achieved the 318 record-high zANET value of 8 × 10-4 at room temperature, which is larger than that for the single-319 crystalline CMG samples, owing to the decrease of κ. The transport measurements and 320 nano/microstructure analysis indicate that the degree of the crystalline order is important for 321 obtaining large SANE. Based on the calculation of the phonon transport spectrum and nanoscale 322 structure analysis, we suggest the importance of the crystal-domain boundary for increasing 323 phonon scatterings to decrease Δκ and κ, which is a different strategy of the conventional 324 phonon engineering using grain boundaries to increase phonon scatterings. Our results 325 demonstrate that the integration of approaches used for development of the conventional 326 thermoelectric materials [69], e.g., phonon engineering, nano-structuring, and fabricating bulk 327 composite, will be also important to improve the performance of the magneto-thermoelectric 328 devices.  329 Acknowledgement 330 The authors thank M. Isomura and K. Suzuki for technical supports, and S. J. Park for 331 fruitful discussion. This work was supported by JST CREST “Creation of Innovative Core 332 Technologies for Nano-enabled Thermal Management” (JPMJCR17I1), JST ERATO 333 “Magnetic Thermal Management Materials” (JPMJER2201), JSPS KAKENHI Grant-in-Aid 334 for Early-Career Scientists (21K14519), JSPS KAKENHI Grant-in-Aid for Scientific Research 335 (S) (22H04965), NEC Corporation, and NIMS Joint Research Hub Program. The computations 336 in the present work were performed using the Numerical Materials Simulator at NIMS. 337 Declaration of Competing Interests 338 The authors declare that they have no known competing financial interests or personal 339 relationships that could have appeared to influence the work reported in this paper.  340   12  Reference 341 [1] C. Fu, Y. Sun, C. Felser, Topological thermoelectrics, APL Mater. 8 (2020) 040913. 342 [2] K. Uchida, W. Zhou, Y. Sakuraba, Transverse thermoelectric generation using magnetic 343 materials, Appl. Phys. Lett. 118 (2021) 140504. 344 [3] K. Uchida, Transport phenomena in spin caloritronics, Proc. Jpn. Acad., Ser. B 97 (2021) 345 69. 346 [4] K. Uchida, J. P. Heremans, Thermoelectrics: From longitudinal to transverse, Joule 6 (2022) 347 2240. 348 [5] K. Elphick, W. Frost, M. Samiepour, T. Kubota, K. Takanashi, H. Sukegawa, S. 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Ed. 48 (2009) 8616.  530   18   531 Fig. 1 (a) Schematic illustration of the measurement setup. (b) H dependence of Ey in the CMG 532 slab sintered at Tsinter = 800℃ and pmax = 60 MPa, i.e., CMG(800, 60), for various values of ∇xT. 533 The inset to (b) shows the M-H curve of CMG(800, 60). The colored dashed lines in (b) show 534 the linear extrapolation with the data in the high H region, where M is saturated (see the M-H 535 curve), for estimating EANE represented as the colored dots at µ0H = 0. (c) ∇xT dependence of 536 EANE. The solid line in (c) shows the result of a linear fitting, of which the slope corresponds to 537 SANE. The error bars represent the 68% confidence level (±s.d.).  538   19  539 Fig. 2 (a-c) H dependence of Ey in the CMG slab sintered at Tsinter = 600℃ (a), at Tsinter = 700℃ 540 (b), and at Tsinter = 800℃ (c). (d) Tsinter, pmax, and Ms dependences of SANE. (e) Tsinter, pmax, and 541 Ms dependences of αxy. The red and blue dashed lines in (d) and (e) correspond to the SANE, αxy, 542 and Ms values obtained in the single-crystalline samples in Refs. 13 and 19, respectively. The 543 error bars represent the 68% confidence level (±s.d.).  544   20  545 Fig. 3 (a-c) Tsinter and pmax dependences of s (a), k (b), and zANET (c) at room temperature (T = 546 300 K). The inset to (b) shows the Tsinter and pmax dependences of Δk. The red and blue dashed 547 lines in (a-c) correspond to the s, k, Δk, and zANET values obtained in the single-crystalline 548 samples in Refs. 13 and 19, respectively. The error bars represent the 68% confidence level 549 (±s.d.). (d) Comparison of zANET between our polycrystalline CMG slab (red bar) and the 550 various bulk magnets (blue bars) around room temperature. zANET for the materials with an 551 asterisk are estimated using the experimental results of the anomalous Ettingshausen effect and 552 the Onsager reciprocal relation.  553   21  Fig. 4 (a, b) SEM-EDS maps for CMG(800, 90) (a) and CMG(800, 30) (b).  554   22  Fig. 5 (a) High-resolution HAADF-STEM image obtained from CMG(800, 90) and electron-555 beam diffraction patterns obtained from the labelled regions. (b) High-resolution HAADF-556 STEM image from CMG(800, 30). (c) High-magnification HAADF-STEM images showing 557 the L21, B2, and modulated phases.  558   23   559 Fig. 6 T dependence of M for CMG(800, 30) and CMG(800, 90) at µ0H = 1 T. The inset shows 560 the averaged values of M in the T range from 5 K to 350 K. 561   562   24  Fig. 7 (a) Calculation of cumulative kph for CMG as a function of L at T = 300 K. (b) SEM 563 images of the fracture surface of CMG(800, 30) and CMG(800, 90). 564