# Fileset [Imamura_main-text_APL25-AR04203R.pdf](https://mdr.nims.go.jp/filesets/2482533a-d305-487b-acdc-a5c67922fa5e/download) ## Creator [Takumi Imamura](https://orcid.org/0009-0003-8005-7591), [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), [Weinan Zhou](https://orcid.org/0000-0003-2946-9913), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051) ## Rights 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 Takumi Imamura, Takamasa Hirai, Weinan Zhou, Yuya Sakuraba, Ken-ichi Uchida; Thermal imaging of anomalous Ettingshausen effect at low temperatures using infrared lock-in thermography. Appl. Phys. Lett. 8 September 2025; 127 (10): 102401 and may be found at https://doi.org/10.1063/5.0279908.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [Thermal imaging of anomalous Ettingshausen effect at low temperatures using infrared lock-in thermography](https://mdr.nims.go.jp/datasets/c7acbfe5-fad1-4e40-8ca4-b7a048822cd6) ## Fulltext Title of Paper Goes Here: Applied Physics Letters ARTICLE scitation.org/journal/apl 1 Thermal imaging of anomalous Ettingshausen effect at low temperatures using infrared lock-in thermography Cite as: Appl. Phys. Lett. XX Submitted: May 2025 Published Online: XX Takumi Imamura,1,2 Takamasa Hirai,2,a) Weinan Zhou,2 Yuya Sakuraba,1,2 and Ken-ichi Uchida1,2,3,a) AFFILIATIONS 1Graduate School of Science and Technology, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan 2National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan 3Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8561, Japan a)Authors to whom correspondence should be addressed: HIRAI.Takamasa@nims.go.jp; UCHIDA.Kenichi@nims.go.jp ABSTRACT Thermal imaging technology has significantly advanced the fields of thermal engineering and fundamental physics by providing precise and non-contact temperature measurements. In the field of spin caloritronics, an active infrared emission microscopy based on the lock-in thermography (LIT) has greatly developed thermoelectric and thermal transport physics in magnetic materials and their hybrid structures, but measurements have been limited to at or above room temperature. Here, we report on the measurements of transverse thermoelectric conversion in a magnetic material, the anomalous Ettingshausen effect (AEE), below room temperature using the LIT technique. Although the infrared emission decreases with decreasing temperature, LIT with the high temperature resolution allows to observe the AEE-induced temperature modulation in a ferromagnetic Heusler alloy Co2MnGa slab down to 200 K and reliably quantify the anomalous Nernst coefficient down to around 240 K. The methodology demonstrated in this work will pave the way for further developments in both fundamental research and practical applications in spin caloritronics. Spin caloritronics is an interdisciplinary field of spintronics and 1 thermal energy engineering and deals with transport phenomena and 2 cross-correlations encompassing electron charge, spin, and heat.1–4 3 This research field was sparked by the discovery of the spin Seebeck 4 effect (SSE) in 2008. SSE refers to the generation of a spin current 5 by applying a temperature gradient to a magnetic material, resulting 6 in an unconventional functionality of thermoelectric conversion that 7 is completely different from the Seebeck effect.5,6 Efforts on early 8 spin caloritronics studies focused on thermally-induced spin 9 transports by extending electrical measurement methods used in 10 spintronics. In contrast, the observation of the spin Peltier effect 11 (SPE),7,8 the Onsager reciprocal of SSE: a temperature modulation 12 as a result of a spin current injection into magnetic materials, caused 13 a stir in this field about 10 years ago. One of the methods that 14 supported to obtain SPE is the lock-in thermography (LIT),8 in which 15 a combination of non-contact thermal imaging through an infrared 16 camera and lock-in detection technique enables highly sensitive 17 temperature measurements with a temperature resolution of <1 mK.9 18 LIT revealed different length and energy scales of thermally and 19 electrically excited spin currents, which contribute to SSE and SPE, 20 respectively, uncovering a physical mechanism that is not just in the 21 simple Onsager reciprocal relation.10 LIT has contributed not only to 22 observation of various unconventional thermoelectric 23 FIG. 1. Schematic of the thermographic measurement configuration. The sample temperature T was controlled by liquid N2 flow and a heater attached to the stage. Thermal images were monitored by an infrared camera through an infrared-transparent CaF2 window. When performing lock-in thermography (LIT) measurements, an ac square-wave-modulated charge current Jc and magnetic field H were applied to the sample. mailto:HIRAI.Takamasa@nims.go.jp Applied Physics Letters ARTICLE scitation.org/journal/apl 2 cooling/heating11–15 and thermal transport16–18 appearing in the 24 presence of a magnetic field and/or magnetization of magnetic 25 materials, but also to quantification of other thermal energy 26 engineering properties.19–26 27 Although the thermographic imaging technique has developed 28 both physics and next-generation thermal management technology, 29 most of the measurements via infrared cameras have been performed 30 at or above room temperature. This is due to the well-known Stefan-31 Boltzmann law, describing that the intensity of infrared emission 32 decays in proportion to the fourth power of the black body’s 33 temperature, which will dramatically reduce the sensitivity of 34 thermal imaging. Furthermore, there are no reports of LIT 35 measurements below room temperature, and it is not yet clear at what 36 temperature range the high-temperature resolution provided by LIT 37 is quantitatively maintained. 38 In this study, we have validated the availability of the LIT 39 technique for measurements of spin-caloritronic phenomena at low 40 temperatures. Here, we focus on measuring the anomalous 41 Ettingshausen effect (AEE),27–29 a transverse magneto-42 thermoelectric effect in magnetic materials, which generates a heat 43 current in the direction of the cross product of an input charge current 44 and spontaneous magnetization. Its Onsager reciprocal, the 45 anomalous Nernst effect (ANE), is one of the most vigorously 46 studied phenomena alongside SSE/SPE in recent spin caloritronics 47 and topological materials science for both physics and device 48 applications.30–38 As a target material for measuring AEE using LIT, 49 we selected a polycrystalline Co2MnGa (CMG) Heusler alloy, which 50 has developed a large transverse thermopower, i.e., anomalous 51 Nernst coefficient SANE comparable to or even larger than that of 52 single crystalline CMG.38–46 By developing the LIT system for low 53 temperature measurements and calibrating the infrared intensity, we 54 ensure the AEE signal in CMG down to about 200 K. The 55 temperature dependence of SANE estimated by the LIT technique 56 shows the consistent trend with that obtained by the conventional 57 thermoelectric measurement down to 240 K, confirming the validity 58 of LIT for spin caloritronics even at low temperatures. 59 The polycrystalline CMG alloy was prepared by a spark plasma 60 sintering technique (the detailed recipe and procedure for sample 61 preparation are described in Ref. 38). First, Co, Mn, and Ga shots 62 were arc-melted in an Ar atmosphere, then the CMG ingot was 63 homogenized in high vacuum at 1000°C. Subsequently, the ingot was 64 crushed using a mortar and planetary ball mill, followed by sieving a 65 powder. Finally, the CMG powder was sintered at 850°C and a 66 pressure of 30 MPa for 60 min under the vacuum condition. 67 Figure 1 shows a schematic of set-up for thermographic 68 measurements in this study. The sample was installed in a custom-69 made sample-in-vacuum liquid N2 cryostat. The CMG slab with a 70 dimension of 0.7 (x) × 10.0 (y) × 3.1 (z) mm was fixed on a sapphire 71 substrate mounted on a Cu stage, in which a heater and resistance 72 temperature sensor were embedded, and the stage temperature was 73 controlled by a temperature controller (Lakeshore 336). Here, the 74 high thermal conductivity of sapphire substrate thermally stabilizes 75 the stage and CMG slab, enabling precise measurements of 76 temperature dependence of thermal responses. The infrared intensity 77 of the sample surface in a high vacuum (<10−4 Pa) was monitored by 78 an infrared camera with an InSb quantum detector (installed in 79 Enhanced Lock-in Thermal Emission: ELITE, DCG Systems G.K.) 80 FIG. 3. Magnetic-field-odd (H-odd) component of lock-in amplitude (Aodd) (a) and phase (φodd) (b) images at T = 250 K, lock-in frequency f = 10 Hz, amplitude of ac square-wave-modulated charge current Jc = 1 A, and μ0|H| = 400 mT, where μ0 is the vacuum permeability. Jc dependence of the Aodd (c) and φodd (d) values at T = 250 K and f = 10 Hz. f dependence of the Aodd (e) and φodd (f) values at T = 250 K and Jc = 1 A. The data points are obtained by averaging the Aodd and φodd signals on the areas defined by the dashed square in (a) and (b), respectively. The error bars represent the standard deviation of the data in the corresponding squares. Solid line in (c) and curve in (e) show the fitting result based on a linear function and one-dimensional heat diffusion equation, respectively. FIG. 2. Sample temperature T dependence of the intensity of infrared emission I and the sensitivity of our LIT system dI/dT. Inset shows curve fitting results for estimating dI/dT. The fitting function is T = a(I−b)c with fitting parameters a, b, and c (015 min) to determine T after the sensor value got stabilized at 91 the target temperature. With the decrease in T, the I value was rapidly 92 reduced, following to the Stefan-Boltzmann law, and the change in I 93 with respect to T also slows down. Note that the finite I signal around 94 200 K is dominantly due to parasitic signals coming from the inside 95 of the infrared camera and lens and does not affect the sensitivity of 96 LIT. By estimating the T dependence of the sensitivity of LIT, dI/dT, 97 it was found that the dI/dT value became zero around 200 K. The 98 magnitude of dI/dT at 200 K was 0.04% of that at 300 K. Thus, we 99 concluded that the lower limit for LIT measurements in this 100 configuration is around 200 K. Note that, the increase in the dI/dT 101 value appears to be saturated at 320 K. This suggests that the high-102 temperature measurement limit of the InSb detector at high 103 temperature is approaching. This can be resolved by changing the 104 integration time of infrared emission, but since high-temperature 105 measurements have been extensively studied in previous research, 106 we will exclude this from the scope of this study. 107 Based on these results, we performed the LIT measurements of 108 AEE in the CMG slab at various T values below 310 K (see 109 supplementary material S1 for detailed configuration of LIT). During 110 the LIT measurements, an ac square-wave-modulated charge current 111 Jc with the frequency f, amplitude Jc, and zero dc offset was applied 112 to the slab along the y axis, where by extracting first harmonic 113 response of thermal images, the thermoelectric contributions (Jc) 114 can be separately extracted from Joule-heating contribution (Jc2: 115 constant in time for such a Jc condition; see also Fig. 1). The detected 116 infrared images were converted into lock-in amplitude A and phase 117 φ images via Fourier analysis, in which the A image shows the 118 magnitude of temperature modulation and the φ image the sign as 119 well as the time delay of the temperature modulation due to the 120 thermal diffusion. Here, when converting the infrared emission to the 121 temperature for A signals at each T, the slope of curve fitting in the 122 inset of Fig. 2 was used. Since the AEE-induced temperature 123 modulation shows the magnetic-field-odd (H-odd) dependence, the 124 complex calculation of Aodd = |A(+H)e−φ(+H) − A(−H)e−φ(−H)|/2 and φodd 125 = −arg[A(+H)e−φ(+H) − A(−H)e−φ(−H)|/2] with the A(+H) [A(−H)] and 126 φ(+H) [φ(−H)] images measured with applying a positive (negative) 127 magnetic field H along the +z (−z) axis can extract the AEE 128 contribution free from the Peltier effect. In this configuration, a heat 129 flow originating from AEE occurs in the x axis, resulting in a uniform 130 temperature change on the sample surface,47 which allows to quantify 131 the anomalous Nernst coefficient independently of thermal boundary 132 conditions between the slab and stage. Figures 3(a) and 3(b) 133 respectively present a result of the low-T LIT measurements: Aodd and 134 φodd images at T = 250 K, f = 10 Hz, Jc = 1 A, and μ0|H| = 400 mT, 135 where μ0 is the vacuum permeability. Note that the value of 400 mT 136 is sufficient for saturating the magnetization of the CMG slab in the 137 z axis at 200−310 K (see supplementary material S2) and the 138 contribution of the ordinary Ettingshausen effect at 400 mT is 139 negligibly small in the CMG slab.38 The uniform Aodd and φodd signals 140 was shown in the sample region. The φodd value of approximately 0°, 141 i.e., the heating signal, under the direction of Jc and H shown in Fig. 142 3(a) corresponds to the positive anomalous Ettingshausen coefficient 143 (= SANET), which is consistent with the sign of SANE of CMG.38–46 144 Figure 3(c) [3(d)] shows the Jc dependence of the Aodd (φodd) values, 145 where Aodd has a linear relationship and φodd is constant with respect 146 to Jc. Figure 3(e) [3(f)] shows the f dependence of the Aodd (φodd) 147 values. With decreasing f, that is, approaching the thermal steady 148 state, Aodd increases slightly and φodd gets closer to 0°. These 149 behaviors obtained below room temperature are consistent with the 150 AEE-induced heat current and its thermal diffusion in the CMG slab 151 with mm-scale dimensions. 152 Next, we take a look at the T dependence. Figure 4(a) [4(b)] 153 shows the Aodd (φodd) images at f = 2 Hz, Jc = 1 A, μ0|H| = 400 mT, 154 and T = 230, 270, and 310 K. Although the Aodd signal gradually 155 decreases with decreasing T due to the reduced sensitivity, the 156 uniform φodd signal independent of T is shown in the three images 157 [see also Figs. 4(c) and 4(d)], indicating that the AEE-induced heat 158 current along the x axis is clearly confirmed by ~230 K. On the other 159 hand, below 230 K, as the T value gets closer to 200 K, the AEE 160 signal can be detected, but the uniformness of the φodd signal 161 dramatically gets worse and the Aodd signal becomes vanishingly 162 small (see supplementary material S3). Therefore, in the quantitative 163 discussion that follows, we will focus on data above 230 K. 164 Finally, we evaluated the SANE value using the equation of SANE 165 = πAoddsκ/2jctT,48,49 where Aodds, κ, jc, and t are the AEE signal 166 FIG. 4. Aodd (a) and φodd (b) images at f = 2 Hz, Jc = 1 A, μ0|H| = 400 mT, and T = 230, 270, and 310 K. T dependence of the Aodd (c) and φodd (d) values at f = 2 Hz and Jc = 1 A. The data points are obtained by averaging the Aodd and φodd signals on the areas defined by the dashed square in the left most panels of (a) and (b), respectively. Applied Physics Letters ARTICLE scitation.org/journal/apl 4 amplitude in the steady state, i.e., at f → 0 Hz, thermal conductivity, 167 amplitude of charge current density, and sample length along the x 168 axis (= 0.7 mm), respectively (see also supplementary material S4). 169 From the T dependence of Aodds estimated by fitting the f dependence 170 of Aodd [Fig. 3(e)] with the solution of the one-dimensional heat 171 diffusion equation in the frequency domain48 and κ measured by the 172 laser flash, differential scanning calorimetry, and Archimedes 173 method in combination (see supplementary material S5), we 174 estimated the T dependence of SANE as shown in Fig. 5. Note that the 175 well-fitted result in Fig. 3(e) also shows that the CMG slab is in a 176 nearly adiabatic condition in the current f range at each temperature. 177 At 300 K, the SANE value is estimated to be 6.2 μV/K, which is 178 comparable to that of single-crystalline bulk CMG39,41 as previous 179 studies have reported.38,43,45 The T dependence of SANE, the slight 180 decrease with decreasing T, and the SANE value at 230 K of 4.0 μV/K 181 also show similar trend to those in previous reports (SANE = 4−5 μV/K 182 in Sakai et al.39 and 4 μV/K in Guin et al.41 for single crystalline 183 CMG and 4 μV/K in Chen et al.45 for polycrystalline CMG at ~230 184 K). However, the steep decrease in SANE around 230−240 K also 185 occurs, which was not reported in previous studies. Therefore, to 186 confirm the validity of our low-T LIT measurements, we 187 quantitatively compared with the conventional method of measuring 188 ANE: measurements of a transverse thermoelectric voltage by 189 applying a temperature gradient to the sample using the Physical 190 Property Measurement System (PPMS-VersaLab, Quantum Design 191 Inc.) and nanovoltmeter (2182A, Keithley). The results of the voltage 192 measurements are also summarized in Fig. 5. Both results are in good 193 agreement, but the steep decrease in the SANE value around 230 K is 194 not shown, suggesting that the quantitative reliability of our LIT 195 method is assured down to around 240 K. 196 In conclusion, we have demonstrated the LIT-based thermal 197 imaging of a spin-caloritronic phenomenon, AEE, below room 198 temperature. We observed the AEE-induced temperature modulation 199 from 310 K to 200 K and revealed the quantitative reliability of the 200 method down to 240 K. Although the value of 240 K is not that low 201 in recent cryogenic research field, there are a number of magnetic 202 materials with their Curie temperature between room temperature to 203 ~200 K, such as ultrathin 3d transition metal films,50,51 magnetic 204 semiconductors,52,53 layered topological materials and van der Waals 205 heterostructures,37,54–57 exhibiting unconventional static and 206 transport properties. One way to extend the temperature range to 207 lower temperatures is to use a different infrared detector. Although 208 InSb is the most commonly used infrared detector in LIT, increasing 209 attention has been directed toward far-infrared-compatible 210 approaches, including HgCdTe-based detectors and quantum well 211 infrared photodetectors. As the temperature of samples decreases, the 212 peak wavelength of the infrared emission shifts toward longer 213 wavelengths. Thus, employing these detectors could potentially 214 allow for LIT measurement at lower temperature than that shown in 215 this study. LIT has a distinct advantage at high-throughput material 216 exploration using chemically composition-spread materials58,59 and 217 spatial-resolved elucidation of non-uniform thermal 218 transport/conversion in artificial-structured composites 219 materials38,60,61 in spin caloritronics, compared with conventional 220 electrical measurements. Our report on the low-temperature LIT 221 method and analysis is versatile even for such materials, experiments, 222 and other spin-caloritronic phenomena [SPE,7,8 the anisotropic 223 magneto-Peltier effect,11 the (anisotropic) magneto-Thomson 224 effect,12,15 the transverse Thomson effect,62 etc; some of them exhibit 225 unconventional behavior that cannot be predicted from electrical 226 measurements based on the Onsager reciprocal relation], which will 227 aid in developing thermal and thermoelectric transport physics as 228 well as spintronic thermal management technology at low 229 temperature. 230 231 See supplementary material for more information about the 232 saturation field of the CMG slab at low temperature, LIT results at T 233 = 200−230 K, and T dependence of κ. 234 235 The authors thank R. Iguchi, F. Ando, S. J. Park, A. Ray, R. 236 Toyama, N. Kojima, H. Yanagihara, and T. Yagi for technical 237 supports and valuable discussions. This work was partially supported 238 by ERATO "Magnetic Thermal Management Materials Project" (No. 239 JPMJER2201) from JST, Japan; Grant-in-Aid for Research Activity 240 Start-up (No. 22K20495) and Grant-in-Aid for Scientific Research 241 (S) (No. 22H04965) from JSPS KAKENHI, Japan; and NEC 242 Corporation. 243 DATA AVAILABILITY 244 The data that support the findings of this study are available 245 from the corresponding author upon reasonable request. 246 REFERENCES 247 1 G. E. W. Bauer, E. Saitoh, and B. J. van Wees, Nat. Mater. 11, 391 (2012). 248 2 S. R. Boona, R. C. Myers, and J. P. Heremans, Energy Environ. Sci. 7, 885 249 (2014). 250 3 K. Uchida, Proc. Jpn. Acad., Ser. B 97, 69 (2021). 251 4 K. Uchida and R. Iguchi, J. Phys. Soc. Japan 90, 122001 (2021). 252 5 K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. 253 Maekawa, and E. Saitoh, Nature 455, 778 (2008). 254 6 K. Uchida, J. Xiao, H. Adachi, J. Ohe, S. Takahashi, J. Ieda, T. Ota, Y. 255 Kajiwara, H. Umezawa, H. Kawai, G. E. W. Bauer, S. Maekawa, and E. 256 Saitoh, Nat. Mater. 9, 894 (2010). 257 7 J. Flipse, F. K. Dejene, D. Wagenaar, G. E. W. Bauer, J. Ben Youssef, and 258 B.J. van Wees, Phys. Rev. Lett. 113, 027601 (2014). 259 8 S. Daimon, R. Iguchi, T. Hioki, E. Saitoh, and K. Uchida, Nat. Commun. 7, 260 13754 (2016). 261 9 O. Breitenstein, W. Warta, and M. Langenkamp, Lock-in Thermography: 262 Basics and Use for Evaluating Electronic Devices and Materials (Springer, 263 Berlin/Heidelberg, Germany 2010). 264 10 A. Takahagi, T. Hirai, R. Iguchi, K. Nakagawara, H. Nagano, and K. 265 Uchida, Appl. Phys. Express 15, 063002 (2022). 266 11 K. Uchida, S. Daimon, R. Iguchi, and E. Saitoh, Nature 558, 95 (2018). 267 12 K. Uchida, M. Murata, A. Miura, and R. Iguchi, Phys. Rev. Lett. 125, 268 106601 (2020). 269 13 T. Hirai, H. Sepehri-Amin, K. Hasegawa, T. Koyama, R. Iguchi, T. Ohkubo, 270 D. Chiba, and K. Uchida, Appl. Phys. Lett. 118, 022403 (2021). 271 14 R. Modak, M. Murata, D. Hou, A. Miura, R. Iguchi, B. Xu, R. Guo, J. 272 Shiomi, Y. Sakuraba, and K. Uchida, Appl. Phys. Rev. 9, (2022). 273 15 R. Modak, T. Hirai, S. Mitani, and K. Uchida, Phys. Rev. Lett. 131, 206701 274 (2023). 275 16 K. Tomioka, K. Uchida, R. Iguchi, and H. Nagano, J. Appl. Phys. 128, 276 215103 (2020). 277 17 Y. Kainuma, R. Iguchi, D. Prananto, V. I. Vasyuchka, B. Hillebrands, T. 278 FIG. 5. T dependence of the anomalous Nernst coefficient SANE estimated by LIT and conventional thermoelectric voltage measurement methods. Applied Physics Letters ARTICLE scitation.org/journal/apl 5 An, and K. Uchida, Appl. Phys. Lett. 118, (2021). 279 18 T. Imamura, T. Hirai, K. Oyanagi, R. Iguchi, K. Takamori, S. Kobayashi, 280 and K. Uchida, Phys. Rev. Appl. 23, 024018 (2025). 281 19 Y. Hirayama, R. Iguchi, X.F. Miao, K. Hono, and K. Uchida, Appl. Phys. 282 Lett. 111, 163901 (2017). 283 20 H. Nakajima, T. Morimoto, Y. Okigawa, T. Yamada, Y. Ikuta, K. Kawahara, 284 H. Ago, and T. Okazaki, Sci. Adv. 5, eaau3407 (2019). 285 21 T. Ishizaki, T. Igami, and H. Nagano, Rev. Sci. Instrum. 91, (2020). 286 22 D. Morelli, R. Marani, E. D’Accardi, D. Palumbo, U. Galietti, and T. 287 D’Orazio, IEEE Trans. Instrum. Meas. 70, 2515214 (2021). 288 23 T. Hirai, R. Iguchi, A. Miura, and K. Uchida, Adv. Funct. Mater. 32, 289 2201116 (2022). 290 24 R. Iguchi, D. Fukuda, J. Kano, T. Teranishi, and K. Uchida, Appl. Phys. 291 Lett. 122, 082903 (2023). 292 25 J. Rittmann and M. Kreutzbruck, Sci. Rep. 13, 17093 (2023). 293 26 P. Liu, A. Alasli, L. Wang, and H. Nagano, Appl. Therm. Eng. 255, 123929 294 (2024). 295 27 T. Seki, R. Iguchi, K. Takanashi, and K. Uchida, Appl. Phys. Lett. 112, 296 152403 (2018). 297 28 J. Wang, Y. K. Takahashi, and K. Uchida, Nat. Commun. 11, 2 (2020). 298 29 P. Wang, W. Xia, J. Shen, Y. Chen, W. Peng, J. Zhang, H. Pan, X. Yu, Z. 299 Liu, Y. Gao, Q. Niu, Z. Xu, H. Yang, Y. Guo, and D. Hou, Natl. Sci. Rev. 11, 300 nwad308 (2024). 301 30 T. Miyasato, N. Abe, T. Fujii, A. Asamitsu, S. Onoda, Y. Onose, N. 302 Nagaosa, and Y. Tokura, Phys. Rev. Lett. 99, 086602 (2007). 303 31 Y. Sakuraba, Scr. Mater. 111, 29 (2016). 304 32 M. Ikhlas, T. Tomita, T. Koretsune, M. T. Suzuki, D. Nishio-Hamane, R. 305 Arita, Y. Otani, and S. Nakatsuji, Nat. Phys. 13, 1085 (2017). 306 33 K. Uchida, W. Zhou, and Y. Sakuraba, Appl. Phys. Lett. 118, 140504 307 (2021). 308 34 T. Asaba, V. Ivanov, S. M. Thomas, S. Y. Savrasov, J. D. Thompson, E. D. 309 Bauer, and F. Ronning, Sci. Adv. 7, eabf1467 (2021). 310 35 Y. Pan, C. Le, B. He, S. J. Watzman, M. Yao, J. Gooth, J. P. Heremans, Y. 311 Sun, and C. Felser, Nat. Mater. 21, 203 (2022). 312 36 F. Ando, T. Hirai, and K. Uchida, APL Energy 2, 016103 (2024). 313 37 S. Noguchi, K. Fujiwara, Y. Yanagi, M. Suzuki, T. Hirai, T. Seki, K. Uchida, 314 and A. Tsukazaki, Nat. Phys. 20, 254 (2024). 315 38 T. Hirai, F. Ando, H. Sepehri-Amin, and K. Uchida, Nat. Commun. 15, 316 9643 (2024). 317 39 A. Sakai, Y. P. Mizuta, A. A. Nugroho, R. Sihombing, T. Koretsune, M. T. 318 Suzuki, N. Takemori, R. Ishii, D. Nishio-Hamane, R. Arita, P. Goswami, and 319 S. Nakatsuji, Nat. Phys. 14, 1119 (2018). 320 40 H. Reichlova, R. Schlitz, S. Beckert, P. Swekis, A. Markou, Y. C. Chen, D. 321 Kriegner, S. Fabretti, G. Hyeon Park, A. Niemann, S. Sudheendra, A. Thomas, 322 K. Nielsch, C. Felser, and S. T. B. Goennenwein, Appl. Phys. Lett. 113, 323 212405 (2018). 324 41 S. N. Guin, K. Manna, J. Noky, S.J. Watzman, C. Fu, N. Kumar, W. 325 Schnelle, C. Shekhar, Y. Sun, J. Gooth, and C. Felser, NPG Asia Mater. 11, 326 16 (2019). 327 42 K. Sumida, Y. Sakuraba, K. Masuda, T. Kono, M. Kakoki, K. Goto, W. 328 Zhou, K. Miyamoto, Y. Miura, T. Okuda, and A. Kimura, Commun. Mater. 329 1, 89 (2020). 330 43 W. Zhou, A. Miura, T. Hirai, Y. Sakuraba, and K. Uchida, Appl. Phys. Lett. 331 122, 062402 (2023). 332 44 R. Uesugi, T. Higo, and S. Nakatsuji, Appl. Phys. Lett. 123, 252401 (2023). 333 45 M. Chen, J. Wang, K. Liu, W. Fan, Y. Sun, C. Felser, and T. Zhu, Adv. 334 Energy Mater. 14, 2400411 (2024). 335 46 K. Oyanagi, H. Sepehri-Amin, K. Takamori, T. Tadano, T. Imamura, R. 336 Nagasawa, K. Mahalingam, T. Hirai, F. Ando, Y. Sakuraba, S. Kobayashi, 337 and K. Uchida, Acta Mater. 296, 121239 (2025). 338 47 R. Das, R. Iguchi, and K. Uchida, Phys. Rev. Appl. 11, 034022 (2019). 339 48 A. Miura, H. Sepehri-Amin, K. Masuda, H. Tsuchiura, Y. Miura, R. Iguchi, 340 Y. Sakuraba, J. Shiomi, K. Hono, and K. Uchida, Appl. Phys. Lett. 115, 341 222403 (2019). 342 49 A. Miura, K. Masuda, T. Hirai, R. Iguchi, T. Seki, Y. Miura, H. Tsuchiura, 343 K. Takanashi, and K. Uchida, Appl. Phys. Lett. 117, 082408 (2020). 344 50 D. Chiba, S. Fukami, K. Shimamura, N. Ishiwata, K. Kobayashi, and T. 345 Ono, Nat. Mater. 10, 853 (2011). 346 51 A. Obinata, Y. Hibino, D. Hayakawa, T. Koyama, K. Miwa, S. Ono, and D. 347 Chiba, Sci. Rep. 5, 14303 (2015). 348 52 Y. Yamada, K. Ueno, T. Fukumura, H.T. Yuan, H. Shimotani, Y. Iwasa, L. 349 Gu, S. Tsukimoto, Y. Ikuhara, and M. Kawasaki, Science 332, 1065 (2011). 350 53 L. Chen, X. Yang, F. Yang, J. Zhao, J. Misuraca, P. Xiong, and S. Von 351 Molnár, Nano Lett. 11, 2584 (2011). 352 54 Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, 353 S. Wu, J. Zhu, J. Wang, X. H. Chen, and Y. Zhang, Nature 563, 94 (2018). 354 55 X. J. Dong, J. Y. You, Z. Zhang, B. Gu, and G. Su, Phys. Rev. B 102, 355 144443 (2020). 356 56 I. A. Verzhbitskiy, H. Kurebayashi, H. Cheng, J. Zhou, S. Khan, Y. P. Feng, 357 and G. Eda, Nat. Electron. 3, 460 (2020). 358 57 H. Zheng, C. Huang, F. Lin, J. Fan, H. Liu, L. Zhang, C. Ma, C. Wang, Y. 359 Zhu, and H. Yang, Appl. Phys. Lett. 122, 023103 (2023). 360 58 H. Masuda, R. Modak, T. Seki, K. Uchida, T.-C. Lau, Y. Sakuraba, R. 361 Iguchi, and K. Takanashi, Commun. Mater. 1, 75 (2020). 362 59 R. Modak, T. Hirai, Y. Sakuraba, S. Mitani, K. Oyanagi, T. Yamazaki, T. 363 Seki, and K. Uchida, Adv. Phys. Res. 3, 2400021 (2024). 364 60 K. Uchida, T. Hirai, F. Ando, and H. Sepehri-Amin, Adv. Energy Mater. 365 14, 2302375 (2024). 366 61 F. Ando, T. Hirai, A. Alasli, H. Sepehri-Amin, Y. Iwasaki, H. Nagano, and 367 K. Uchida, Energy Environ. Sci. 18, 4068 (2025). 368 62 A. Takahagi, T. Hirai, A. Alasli, S.J. Park, H. Nagano, and K. Uchida, Nat. 369 Phys. (2025); doi: 10.1038/s41567-025-02936-3. 370 371