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## Creator

Huiling Mao, [Yuta Sasaki](https://orcid.org/0000-0002-9192-4799), Yuta Kobayashi, [Shinji Isogami](https://orcid.org/0000-0001-7230-6090), Teruo Ono, Takahiro Moriyama, [Yukiko K. Takahashi](https://orcid.org/0000-0001-9197-7236), Kihiro T. Yamada

## 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 Mao, H., Sasaki, Y., Kobayashi, Y., Isogami, S., Ono, T., Moriyama, T., ... & Yamada, K. T. (2023). Ultrafast spin-to-charge conversion in antiferromagnetic (111)-oriented L12-Mn3Ir. Applied Physics Letters, 123(21) and may be found at https://doi.org/10.1063/5.0168138[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Ultrafast spin-to-charge conversion in antiferromagnetic (111)-oriented L12-Mn3Ir](https://mdr.nims.go.jp/datasets/3a94264a-a493-4398-917e-1cffda7967f9)

## Fulltext

Microsoft Word - MH_APL_main _revised.docx1  Ultrafast spin-to-charge conversion in antiferromagnetic (111)-oriented L12-Mn3Ir 1 Huiling Mao,1 Yuta Sasaki,2 Yuta Kobayashi,3 Shinji Isogami,2 2  Teruo Ono,3,4 Takahiro Moriyama,5,6 Yukiko K. Takahashi,2 and Kihiro T. Yamada1, a) 3 1) Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan 4 2) National Institute for Materials Science, Tsukuba, Ibaraki 987-6543, Japan 5 3) Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan 6 4) Center for Spintronics Research Network, Institute for Chemical Research, Kyoto University, Uji, Kyoto, 611-0011, Japan 7 5) Department of Materials Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan 8 6) PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama 322-0012, Japan 9 a) Author to whom correspondence should be addressed: yamada@phys.titech.ac.jp 10  11 Antiferromagnetic L12-Mn3Ir combines outstanding spin-transport properties with magnons in the terahertz (THz) frequency 12 range. However, the THz radiation emitted by ultrafast spin-to-charge conversion via the inverse spin Hall effect remains 13 unexplored. In this study, we measured the THz emission and transmission of a permalloy/(111)-oriented L12-Mn3Ir multilayer 14 by THz time-domain spectroscopy. The spin Hall angle was determined to be approximately constant at 0.035 within a 15 frequency range of 0.3–2.2 THz, in comparison with the THz spectroscopy of a permalloy/Pt multilayer. Our results not only 16 demonstrate the potential of L12-Mn3Ir as a spintronic THz emitter but also provide insights into the THz spin transport 17 properties of L12-Mn3Ir. 18 A spintronic terahertz (THz) emitter is a device that emits single-cycle THz electromagnetic waves through ultrafast spin-to-19 charge conversion in a heavy metal layer coupled to a ferromagnetic metal.1-3 The irradiation of a femtosecond laser pulse to 20 the heterostructure triggers ultrafast demagnetization and flow of hot electrons inside the ferromagnetic layer, producing a spin 21 current pulse with a sub-picosecond duration.4,5 The spin current pulse is then converted into charge current, resulting in single-22 cycle THz electromagnetic wave emissions.1-3 Spintronic THz emitters with Pt and W2,6 are already commercialized and 23 comparable to THz crystals in terms of the bandwidth and flexibility.3 Because the efficiency of the THz-emission process 24 depends on the spin Hall (SH) angle of the spin-to-charge conversion layer,7 much effort is being made to develop spintronic 25 THz emitters from new materials with larger SH angles and new functionalities. 26 Antiferromagnets have recently emerged as promising candidates for spintronic devices operating in the THz frequency 27 range. Noncollinear antiferromagnets of Mn3X (X = Sn, Ge, Pt, Ga, Ir, and Rh) exhibit large anomalous Hall and magneto-28 optical Kerr effects,8-20 due to the spin-orbit coupling (SOC) and noncollinear spin textures.19,20 Among these compounds, Mn3Ir 29 2  has a particularly high SH conductivity owing to its strong SOC.21,22 Unlike the γ-phase disordered alloy Mn100-xIrx,23 the L12-30 ordered phase of Mn3Ir has a face-centered cubic lattice with an all-in/all-out triangular spin structure in the (111) lattice plane 31 (Fig.1(a)) as a result of the competition between the magnetic frustration and exchange interactions.24,25 The L12-ordered phase 32 of Mn3Ir exhibits a high Néel temperature of ~960 K.25 The ordered triangular magnetic configuration with such high thermal 33 stability can play a major role in imposing an exchange bias on a ferromagnetic layer in a spin valve structure employed as a 34 read head of a hard disk drive.26 However, despite its potential, the capability of L12-ordered antiferromagnetic Mn3Ir as a 35 spintronic THz emitter is yet to be explored, in contrast to conventional heterostructures that utilize nonmagnetic heavy 36 metals.27-30 In this paper, we report the observation of THz-wave emissions resulting from the ultrafast spin-to-charge 37 conversion in an L12-Mn3Ir film. By comparing the THz emission spectra with the spectra of Pt, we quantified the SH angle of 38 L12-Mn3Ir in the THz spectral range, which was determined to be almost constant at 0.024 up to a frequency of 2.2 THz.  39 We deposited a 15 nm-thick L12-ordered Mn3Ir film epitaxially grown on a MgO(111) substrate at 600 °C by direct current 40 sputtering. Previous studies have demonstrated that Mn3Ir films prepared under similar deposition conditions exhibited a sizable 41 anomalous Hall effect. 12,13,14 Moreover, we deposited a 3 nm-thick permalloy (Py) layer as the spin current source. The 42 multilayer was protected from oxidation by a 5 nm-thick SiO2 capping layer. We also prepared Py(3 nm)/Pt(5 nm) and Pt(3 43 nm)/Mn3Ir(15 nm) on MgO(111) substrates as control samples using the same sputtering system. The crystal structures of the 44 films were analyzed by X-ray diffraction (XRD). Figure 1(b) shows the out-of-plane θ-2θ XRD profile of the Py/Mn3Ir 45 multilayer, measured using Kα1(Cu) X-ray source. The out-of-plane XRD profile without any secondary peaks indicates the 46 epitaxial growth of the Mn3Ir film on the MgO (111) substrate. To evaluate the magnitude of L12 ordering of the Mn3Ir film, 47 we measured the X-ray reflection of the L12-Mn3Ir (001) and (002) planes with a tilt angle of 54.7° with respect to the (111) 48 plane. Notably, the X-ray reflection of the L12-Mn3Ir (001) and (002) planes correspond to the superlattice and fundamental 49 diffraction peaks, respectively.31 The results are shown in Fig. 1(c). The order parameter, �, was calculated using the following 50 equation: 31,32 51 where ����  and ����  are the integrated values of the (001) and (002) peaks at a diffraction angle of 2����  and 2���� , 52 respectively. The structure factors of the superlattice peak,  �  + 3�
�, and the fundamental peak, �  − �
�, were calculated 53 using the atomistic scattering factors, �  = 77 and  �
� = 25, respectively. We also considered the angular dependences of the 54 Lorentz-polarization factor, ����� = �1 + cos�2��/sin��cos�, and the absorption factor, ���� = �1 − ��  !"#$%&�/2', with the 55 � = (������  + 3�
������������������������  − �
������������������ , (1) 3  absorption coefficient, ' = 0.251 μm-1. The order parameter calculated using Eq. (1) was � = 0.33. The calculated interplanar 56 spacing for the (111) plane was *��� = 0.2182 nm, which was close to that of bulk Mn3Ir, *��� = 0.2181 nm. By contrast, the 57 lattice parameter along the oblique [001] direction was 0.3807 nm, which was larger than the bulk lattice parameter of 0.3778 58 nm. This indicates the presence of in-plane tensile strain by the deposition to the MgO (111) substrate due to the lattice mismatch 59 of ~9 % between Mn3Ir and MgO. We have also observed the twinning of the Mn3Ir crystal in the XRD φ-scan data (Fig. 1(e)) 60 in comparison with that of the MgO (002) peak (Fig. 1(d)). The twinning percentage determined from the φ XRD scan of the 61 (002) peak (Fig. 1(d)) was 34%. 62 0.05.010.020 30 40 500.00.81.60 60 120 180 240 300 3600.00.81.60.03.06.0Intensity, I (×103 count/s) MgO(111)Mn3Ir (111)∗(c)∗ ∗ ∗2θ (° )Mn3Ir (002)Mn3Ir (001)SiO2MgO(002)∗(b)(a)[111]MnIrϕ (° )I (×103 count/s)(e)MgO (002)Mn3Ir (002)I (×105 count/s)(d) 63 FIG. 1. (a) Crystal and spin structure of L12-Mn3Ir. (b) θ-2θ XRD pattern of the Py/Mn3Ir/MgO (111) sub. (c) θ-2θ X-ray 64 reflection pattern of the same sample measured under a tilt angle of 54.7° from the direction normal to the (111) plane. XRD 65 φ-scans of the (d) (002) diffraction peak of the MgO substrate and (e) (002) diffraction peak of the Mn3Ir layer. Here, the 66 asterisk symbols indicate the diffractions from a sample mount made of clay. 67  68 For the THz emission and transmission experiments, we employed a Yb: KGW laser system with a central wavelength, 69 repetition frequency, and pulse width of 1028 nm, 10 kHz, and 230 fs, respectively. Using a permanent magnet, we applied an 70 in-plane magnetic field of ±0.5 kOe to a multilayer for saturating the magnetization of the Py layer. The pump pulses were 71 modulated using an optical chopper at 570 Hz, enabling the detection of pump-induced THz signals by a lock-in amplifier. We 72 detected the THz waves through changes in the ellipticity of a probe pulse by the electro-optic effect of an 800 µm thick 73 CdTe(110) crystal. The THz emission and detection processes were performed in a dry nitrogen environment at room 74 temperature. See Ref. 30 for further details on the measurement configuration. 75 By exciting the sample with linearly polarized pulses, the spin currents flowed from the Py layer to the Mn3Ir layer, 76 generating THz waves (Fig. 2(a)). Figure 2(b) shows the THz emission signals, +,-./�0�, acquired when applying a magnetic 77 field, H = +0.5 kOe and −0.5 kOe, to the Py/Mn3Ir and Pt/Mn3Ir multilayers. The polarity of the THz waves originating from 78 4  the Py/Mn3Ir multilayer was inverted when the H-direction was reversed. By contrast, no signal was observed for the Pt/Mn3Ir 79 multilayer. The magnetic dipole emission33 from the Py single layer is much weaker than the electric dipole emission from the 80 Py/Mn3Ir multilayer via the spin-charge-conversion mechanism (see Supplementary Material). These results indicate that THz 81 waves from the Py/Mn3Ir multilayer are induced by spin currents resulting from ultrafast demagnetization of the Py layer. 82 Contrastingly, the Mn3Ir layer acts as an ultrafast spin-to-charge converter but not as a spin-current source, as similarly reported 83 in to the case of Mn3Sn34.  In addition, the fluence dependence of the normalized peak intensity shows that the THz emission 84 intensity, +,-./�0�, monotonically increases within the limit of the fluence range used in this study (Fig. 2(c)). To measure the 85 time-reversal odd component of the SH angle,17,21,35 we applied an out-of-plane magnetic field of 140 kOe, which was 86 sufficiently large to obtain a minor hysteresis response in the anomalous Hall effect13, to the Py/Mn3Ir multilayer using a 87 superconducting magnet. Subsequently, we measured +,-./�0� using our THz emission set-up. However, we did not find any 88 meaningful changes in +,-./�0� before and after applying the magnetic field of 140 kOe. This independence can be attributed 89 to the small remanence magnetization, multidomain state, and crystal twinning of the Mn3Ir film.  90 -2 -1 0 1 2-0.2-0.10.00.10.20 1 2 30.00.51.0Semit (t) (mV) Delay time, t (ps) +H -H        Pt/Mn3IrPy/Mn3Ir(b)(c)Speakemit (norm.)Fluence (mJ/cm2)(a) 91 FIG. 2. (a) Schematic of the THz emission from spin-to-charge conversion inside the L12-Mn3Ir. (b) THz-emission signals 92 (+,-./�0�) of the Py/Mn3Ir (solid lines) and Pt/Mn3Ir (dashed lines) under an external magnetic field (H) of ±0.5 kOe. (b) Here, 93 the pump fluence was set at 2.94 mJ/cm2. (c) Pump fluence dependence of the peak intensity of +,-./�0�. The dependency was 94 normalized based on the data obtained with a pump fluence of 2.94 mJ/cm2. 95  96 The THz electric field, 1�2�, generated by the spin-to-charge conversion effects can be described in terms of the angular 97 frequency domain as follows:7,36,37 98 5  where �, ℏ, 4, and 5 represent the electron charge, Dirac constant, unit vector normal to the film plane, and spin unit vector, 99 respectively. The parameters �67, 89:, and 06; denote the SH angle, spin diffusion length, and thickness of the spin-to-charge 100 conversion layer, respectively. The direction of the 5 vector is parallel to the localized spin direction of the ferromagnetic layer. 101 Here, we neglected the longitudinal spin-to-charge conversions. The density of spin current created through the demagnetization 102 of the ferromagnetic layer, <9:,-=>�2�, was assumed to be linearly proportional to the magnetization component parallel to an 103 external magnetic field and absorbed fluence, ��?@-?, where � and �?@-? are the absorption rate and pump fluence. The 104 magnetizations of the Py/Mn3Ir and Py/Pt multilayers are 531 ± 14 emu/cm3 and 770 ± 11 emu/cm3 at 0.5 kOe, respectively. 105 The absorption rates of the Py/Mn3Ir and Py/Pt multilayers were � = 0.512 and 0.408, respectively, which are estimated by 106 measuring the transmission and reflectance of the pump light. See Supplementary Material for the magnetic hysteresis loop 107 and details of estimating �. 108    The complex transmittance in the angular frequency domain, AB�2�, was calculated by the following equation:7,30,38  109 where +/=�9�2� is the amplitude of the complex fast Fourier transform (FFT) of the THz transmission signal. The phase and 110 amplitude changes according to the difference in substrate thickness, ∆*9@D , are included in the phase, ∆E = 111 F�GH9@D�2� − G��∆*9@D2/I, where GH9@D�2�, G�, and I denote the refractive index of the substrate, refractive index of air, and 112 speed of light, respectively. Combining Eqs. (2) and (3), we can estimate the value of �67 by considering the results of the 113 transmission experiments obtained for the control samples, Py/Pt multilayer, and bare MgO substrate. Figures 3(a) and (b) show 114 the +/=�9�0� and FFT spectra, |+/=�9�2�|, respectively. To estimate the ∆E in Eq. (3), we used G� = 1, and the frequency 115 dependence of GH9�2� (Ref. 29). The actual measurement values of ∆*9@D were −0.031 mm and 0.007 mm for the Py/Mn3Ir 116 and Py/Pt multilayers, respectively.  117 1�2� ∝ AB�2� 2�ℏ �67�2�<9:,-=>�2� 89:06; tanh 06;289: 4 × 5, (2) AB�2� = +/=�9P.Q- �2�+/=�99@D �2� ��RST , (3) 6   118 FIG. 3 (a) THz transmission signals �+/=�9�0�) of the Py/Mn3Ir multilayer (red), Py/Pt reference multilayer (blue), and bare 119 MgO (111) substrate (light green). (b) Fast Fourier transform (FFT) spectra (|+/=�9�2�|) of the samples. (c) THz emission 120 signals and (d) FFT spectra (|+,-./�2�|) of the Py/Mn3Ir and Py/Pt multilayers. The inset numbers indicate the multiplication 121 factors. The error bars in the spectra were estimated from the standard errors of the signals.  122 The THz wave emission signals of the Py/Mn3Ir and Py/Pt multilayers are shown in Fig. 3(c). To estimate the �67 values 123 of the Mn3Ir layer, the ratio of the FFT spectra in Fig. 3(d), |+,-./�2�|, and the real part of AB�2� were substituted in Eq. (2). 124 The sign of �67 at each frequency was determined by considering the phase information of FFT. Here, we assumed that the 125 following parameters were constant within the frequency range: �67 = 0.12 and 89: = 1.4 nm for the Pt layer39, and 89: = 126 1.0 nm for the Mn3Ir layer.40 We ignored the spin-to-charge conversion in the Py layer because of the small SH angle, i.e., 127 �67 =  0.005.41 The �67  values in the THz frequency range of this work can then be analyzed by THz emission and 128 transmission spectroscopy. The results of these analyses are shown in Fig. 4. The �67 values first increased within a frequency 129 range of 0.15–0.30 THz, whereas they remained nearly constant at 0.035 up to a frequency of 2.2 THz. Ab initio calculations 130 may explain the frequency dependence of the intrinsic spin Hall effect. We propose that the dispersion of �67 is effective to 131 observe the modulation of the spin Hall effect by magnons42,43 and phonons44 of other antiferromagnets in the THz frequency 132 range. In addition, the estimated spin Hall angle for our Mn3Ir film, �67 = 0.024, was smaller compared with those (0.10–0.15) 133 obtained from transport experiments of (111)-oriented and polycrystalline disordered Mn3Ir films.40 Theoretical calculations 134 predicted a large negative SH conductivity of L12-Mn3Ir.22,40 The net �67 of our Mn3Ir film may be small because of the 135 mixture of L12-ordered and disordered Mn3Ir crystals with the spin Hall effects of opposite signs. Investigating the order-136 parameter dependence of the THz emission will be valuable to uncover the origin of the THz emission, which would lead us to 137 further enhance the spin-conversion efficiency of Mn3Ir systems.  138 -60612180510152025-3 -2 -1 0 1 2 3 4 5-303690 1 2 3 4048121620Strans (t) (mV)×2×2(a) Strans (ω) (mV)  MgO sub. Py/Mn3Ir Py/Pt(b)Semit (t) (mV)t (ps)×12(c) Semit (ω) (mV)Frequency, ω / 2π (THz)×12(d)7  0.0 0.5 1.0 1.5 2.0 2.50.000.020.040.06Spin Hall angle θSH (arb. unit)ω / 2π (THz) 139 FIG. 4. Frequency dependence of spin Hall angle for the (111)-ordered L12-Mn3Ir film. The error bars were estimated from the 140 standard errors of the THz transmission (Fig. 2(b)) and emission (Fig. 2(d)) spectra. 141 In this study, we investigated the THz emissions resulting from ultrafast spin-to-charge conversions via the inverse spin 142 Hall effect in a (111)-oriented L12-Mn3Ir thin film on a MgO(111) substrate. Based on the XRD profiles, we found that the 143 Mn3Ir layer had an L12 ordering of 0.33 and was distorted in the in-plane direction due to the lattice mismatch with the 144 MgO(111) substrate. Our control experiments revealed that the Mn3Ir layer was not a spin source but a spin-to-charge converter 145 in the current experimental configuration. By comparing the THz wave emission and transmission results for the Py/Mn3Ir 146 multilayer with those for the Py/Pt multilayer, the spin Hall angle of the Mn3Ir layer was calculated to be ~0.035 within the 147 THz frequency range investigated in this study. We believe that our results and methodology will be useful in the search for 148 promising antiferromagnets for THz spintronic applications.  149 See the Supplementary Material for additional details on the ultrafast terahertz measurement setup, transmission and 150 reflectance of the pump light, and analysis of the THz emission spectrum. 151 AUTHOR DECLARATIONS 152 Conflict of interest 153 The authors have no conflicts to disclose. 154  155 DATA AVAILABILITY 156 The data that support the findings of this study are available from the corresponding author upon reasonable request. 157  158 8  ACKNOWLEDGMENTS 159 We thank Prof. H. Munekata, Prof. T. Satoh, and Dr. D. Bossini for critically reading the manuscript and Dr. Y. Takamura and 160 Prof. S. Nakagawa for technical guidance in the XRD measurements. This work was partly supported by JSPS KAKENHI 161 (Grant nos. 22K14588, 21K14218, and 21H04562), Sasakawa Scientific Research Grant (Grant no. 2023-2032), JST 162 PRESTO (Grant nos. JPMJCR22C3 and JPMJPR20B9), and the Collaborative Research Program of the Institute for 163 Chemical Research, Kyoto University. 164  165 REFERENCES 166 1T. Kampfrath, M. Battiato, P. Maldonado, G. Eilers, J. Nötzold, S. Mährlein, V. Zbarsky, F. Freimuth, Y. Mokrousov, S. Blügel, 167 M. Wolf, I. Radu, P. M. Oppeneer, and M. Münzenberg, Nat. Nanotechnol. 8, 256–260 (2013) [DOI: 168 10.1038/nnano.2013.43]. 169 2T. Seifert, S. Jaiswal, U. Martens, J. Hannegan, L. Braun, P. Maldonado, F. Freimuth, A. Kronenberg, J. Henrizi, I. Radu, E. 170 Beaurepaire, Y. Mokrousov, P. M. Oppeneer, M. Jourdan, G. Jakob, D. Turchinovich, L. M. Hayden, M. Wolf, M. 171 Münzenberg, M. Kläui, and T. Kampfrath, Nat. Photonics 10, 483–488 (2016) [DOI: 10.1038/nphoton.2016.91]. 172 3E. T. Papaioannou and R. Beigang, Nanophotonics 10, 1243–1257 (2020) [DOI: 10.1515/nanoph-2020-0563]. 173 4M. Battiato, K. Carva, and P. M. Oppeneer, Phys. Rev. Lett. 105, 027203 (2010) [DOI: 10.1103/PhysRevLett.105.027203]. 174 5D. Rudolf, C. L.-O-Vorakiat, M. Battiato, R. Adam, J. M. Shaw, E. Turgut, P. Maldonado, S. Mathias, P. Grychtol, H. T. 175 Nembach, T. J. Silva, M. Aeschlimann, H. C. Kapteyn, M. M. Murnane, C. M. Schneider, and P. M. Oppeneer, Nat. 176 Commun. 3, 1037 (2012) [DOI: 10.1038/ncomms2029]. 177 6D. Kong, X. Wu, B. Wang, T. Nie, M. Xiao, C. Pandey, Y. Gao, L. Wen, W. Zhao, C. Ruan, J. Miao, Y. Li, and W. Li, Adv. 178 Opt. Mater. 7, 1900487 (2019) [DOI: 10.1002/adom.201900487]. 179 7T. S. Seifert, N. M. Tran, O. Gueckstock, S. M. Rouzegar, L. Nadvornik, S. Jaiswal, G. Jakob, V. V. Temnov, M. Münzenberg, 180 M. Wolf, M. Kläui, and T. Kampfrath, J. Phys. D: Appl. Phys. 51, 364003 (2018) [DOI: 10.1088/1361-6463/aad536]. 181 8S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212–215 (2015) [DOI: 10.1038/nature15723]. 182 9N. Kiyohara, T. Tomita, and S. Nakatsuji, Phys. Rev. Appl. 5, 064009 (2016) [DOI: 10.1103/PhysRevApplied.5.064009]. 183 10A. K. Nayak, J. E. Fischer, Y. Sun, B. Yan, J. Karel, A. C. Komarek, C. Shekhar, N. Kumar, W. Schnelle, J. Kübler, C. Felser, 184 and S. S. P. Parkin, Sci. Adv. 2, e1501870 (2016) [DOI: 10.1126/sciadv.1501870]. 185 11Z. Q. Liu, H. Chen, J. M. Wang, J. H. Liu, K. Wang, Z. X. Feng, H. Yan, X. R. Wang, C. B. Jiang, J. M. D. Coey, and A. H. 186 MacDonald, Nat. Electron. 1, 172–177 (2018) [DOI: 10.1038/s41928-018-0040-1]. 187 9  12H. Iwaki, M. Kimata, T. Ikebuchi, Y. Kobayashi, K. Oda, Y. Shiota, T. Ono, and T. Moriyama, Appl. Phys. Lett. 116, 022408 188 (2020) [DOI: 10.1063/1.5128241]. 189 13Y. Kobayashi, M. Kimata, D. Kan, T. Ikebuchi, Y. Shiota, H. Kohno, Y. Shimakawa, T. Ono, and T. Moriyama, Jpn. J. Appl. 190 Phys. 61, 070912 (2022) [DOI: 10.35848/1347-4065/ac7625]. 191 14Y. Kobayashi, T. Ikebuchi, Y. Shiota, T. Ono, and T. Moriyama, J. Phys. Soc. Jpn. 45, 75–78 (2021) [DOI: 192 10.3379/msjmag.2107L002]. 193 15T. Matsuda, N. Kanda, T. Higo, N. P. Armitage, S. Nakatsuji, and R. Matsunaga, Nat. Commun. 11, 909 (2020) [DOI: 194 10.1038/s41467-020-14690-6]. 195 16X. Li, L. Xu, L. Ding, J. Wang, M. Shen, X. Lu, Z. Zhu, and K. Behnia, Phys. Rev. Lett. 119, 056601 (2017) [DOI: 196 10.1103/PhysRevLett.119.056601]. 197 17M. Kimata, H. Chen, K. Kondou, S. Sugimoto, P. K. Muduli, M. Ikhlas, Y. Omori, T. Tomita, A. H. MacDonald, S. Nakatsuji, 198 and Y. Otani, Nature 565, 627–630 (2019) [DOI: 10.1038/s41586-018-0853-0]. 199 18M. Ikhlas, T. Tomita, T. Koretsune, M.-T. Suzuki, D. Nishio-Hamane, R. Arita, Y. Otani, and S. Nakatsuji, Nat. Phys. 13, 200 1085–1090 (2017) [DOI: 10.1038/nphys4181]. 201 19H. Chen, Q. Niu, and A. H. MacDonald, Phys. Rev. Lett. 112, 017205 (2014) [DOI: 10.1103/PhysRevLett.112.017205]. 202 20M.-T. Suzuki, T. Koretsune, M. Ochi, and R. Arita, Phys. Rev. B 95, 094406 (2017) [DOI: 10.1103/PhysRevB.95.094406]. 203 21J. Železný, Y. Zhang, C. Felser, and B. Yan, Phys. Rev. Lett. 119, 187204 (2017) [DOI: 10.1103/PhysRevLett.119.187204]. 204 22Y. Zhang, Y. Sun, H. Yang, J. Železný, S. P. P. Parkin, C. Felser, and B. Yan, Phys. Rev. B 95, 075128 (2017). 205 23T. Yamaoka, J. Phys. Soc. Jpn. 36, 445–450 (1974) [DOI: 10.1143/JPSJ.36.445]. 206 24A. B. Harris, C. Kallin, and A. J. Berlinsky, Phys. Rev. B 45, 2899–2919 (1992) [DOI: 10.1103/PhysRevB.45.2899]. 207 25I. Tomeno, H. N. Fuke, H. Iwasaki, M. Sahashi, and Y. Tsunoda, J. Appl. Phys. 86, 3853–3856 (1999) [DOI: 208 10.1063/1.371298]. 209 26H. Takahashi, Y. Kota, M. Tsunoda, T. Nakamura, K. Kodama, A. Sakuma, and M. Takahashi, J. Appl. Phys. 110, 123920 210 (2011) [DOI: 10.1063/1.3672450]. 211 27M. B. Jungfleisch, Q. Zhang, W. Zhang, J. E. Pearson, R. D. Schaller, H. Wen, and A. Hoffmann, Phys. Rev. Lett. 120, 207207 212 (2018) [DOI: 10.1103/PhysRevLett.120.207207]. 213 28Y. Wu, M. Elyasi, X. Qiu, M. Chen, Y. Liu, L. Ke, and H. Yang, Adv. Mater. 29, 1603031 (2017) [DOI: 214 10.1002/adma.201603031]. 215 10  29D. M. Nenno, L. Scheuer, D. Sokoluk, S. Keller, G. Torosyan, A. Brodyanski, J. Lösch, M. Battiato, M. Rahm, R. H. Binder, 216 H. C. Schneider, R. Beigang, and E. Th. Papaioannou, Sci. Rep. 9, 13348 (2019) [DOI: 10.1038/s41598-019-49963-8]. 217 30Y. Sasaki, Y. Takahashi, and S. Kasai, Appl. Phys. Express 13, 093003 (2020) [DOI: 10.35848/1882-0786/abb1c9]. 218 31A. A. Jara, I. Barsukov, B. Youngblood, Y. Chen, J. Read, H. Chen, P. Braganca, and I. N. Krivorotov, IEEE Magn. Lett. 7, 219 1–5 (2016) [DOI: 10.1109/LMAG.2016.2590464]. 220 32B. D. Cullity and S. R. Stock, Elements of X-Ray Diffraction, 3rd ed. (Prentice Hall, 2001) [DOI: 10.1119/1.1934486].  221 33E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, Appl. Phys. Lett. 84, 3465-222 3467 (2004) [DOI: 10.1063/1.1737467]. 223 34J. Holanda, H. Saglam, V. Karakas, Z. Zang, Y. Li, R. Divan, Y. Liu, O. Ozatay, V. Novosad, J. E. Pearson, and A. 224 Hoffmann, Phys. Rev. Lett. 124, 087204 (2020) [DOI: 10.1103/PhysRevLett.124.087204]. 225 35X. Zhou, B. Song, X. Chen, Y. You, S. Ruan, H. Bai, W, Zhang, G. Ma, J. Yao, F. Pan, Z. Jin, and C. Song, Appl. Phys. 226 Lett. 115, 182402 (2019) [DOI: 10.1063/1.5121384]. 227 36A. Azevedo, L. H. Vilela-Leão, R. L. Rodríguez-Suárez, A. F. Lacerda Santos, and S. M. Rezende, Phys. Rev. B 83, 144402 228 (2011) [DOI: 10.1103/PhysRevB.83.144402]. 229 37J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Rev. Mod. Phys. 87, 1213–1260 (2015) [DOI: 230 10.1103/RevModPhys.87.1213]. 231 38L. Duvillaret, F. Garet, and J. L. Coutaz, IEEE J. Sel. Top. Quantum Electron. 2, 739 (1996) [DOI: 10.1109/2944.571775]. 232 39M. Obstbaum, M. Härtinger, H. G. Bauer, T. Meier, F. Swientek, C. H. Back, and G. Woltersdorf, Phys. Rev. B 89, 060407 233 (2014) [DOI: 10.1103/PhysRevB.89.060407]. 234 40W. Zhang, W. Han, S. H. Yang, Y. Sun, Y. Zhang, B. Yan, and S. S. P. Parkin, Sci. Adv. 2, e1600759 (2016) [DOI: 235 10.1126/sciadv.1600759]. 236 41A. Tsukahara, Y. Ando, Y. Kitamura, H. Emoto, E. Shikoh, M. P. Delmo, T. Shinjo, and M. Shiraishi, Phys. Rev. B 89, 237 235317 (2014) [DOI: 10.1103/PhysRevB.89.235317]. 238 42J. Li, C. B. Wilson, R. Cheng, M. Lohmann, M. Kavand, W. Yuan, M. Aldosary, N. Agladze, P. Wei, M. S. Sherwin, and J. 239 Shi, Nature 578, 70–74 (2020) [DOI: 10.1038/s41586-020-1950-4]. 240 43P. Vaidya, S. A. Morley, J. van Tol, Y. Liu, R. Cheng, A. Brataas, D. Lederman, and E. del Barco, Science 368, 160–165 241 (2020) [DOI: 10.1126/science.aaz4247]. 242 44T. Kawada, M. Kawaguchi, T. Funato, H. Kohno, and M. Hayashi, Sci. Adv. 7, eabd9697 (2021) 243 [DOI:10.1126/sciadv.abd9697]. 244