# Fileset [MDR.pdf](https://mdr.nims.go.jp/filesets/18040432-02e8-41d6-a012-8972ed6fb368/download) ## Creator [Shinji Isogami](https://orcid.org/0000-0001-7230-6090), Mitsuru Ohtake, [Yusuke Kozuka](https://orcid.org/0000-0001-7674-600X), [Yukiko K. Takahashi](https://orcid.org/0000-0001-9197-7236) ## Rights [Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/) ## Other metadata [Wide modulation of coercive fields in Mn4N ferrimagnetic thin films caused dominantly by dislocation microstructures](https://mdr.nims.go.jp/datasets/70139276-9173-49fc-a716-a28d157ce391) ## Fulltext 1 Wide modulation of coercive fields in Mn4N ferrimagnetic thin films caused dominantly by dislocation microstructures Shinji Isogami1*, Mitsuru Ohtake2, Yusuke Kozuka1, and Yukiko K. Takahashi1 1 Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, Sengen 1-2-1, Tsukuba, Ibaraki, 305-0047 Japan 2 Faculty of Engineering, Yokohama National University, Tokiwadai 79-5, Hodogaya, Yokohama, Kanagawa, 240-8501 Japan *E-mail: isogami.shinji@nims.go.jp Perpendicular magnetic anisotropy and coercive fields (Hc) are governed by the degree of order of N (S) in ferrimagnetic Mn4N thin films. However, in this study, we observed non-negligible modulation of Hc extending from 10 to 7.5 kOe for three Mn4N films grown at a substrate temperature (Tsub) in the range of 400–500 C, even with identical S, which has not been discussed to date. The possible mechanisms for this phenomenon were explored by transport properties and fine structural analysis. The results indicated that longitudinal resistivity and anomalous Hall resistivity remain unchanged for three Mn4N films. Conversely, the number of 2 dislocations and in-plane grain size (D) increased, whereas the residual strain () decreased with increasing Tsub. This indicates that Hc of the Mn4N film with the same S is sensitive to the variation in dislocations, D and . Tunable Hc of this type can be effectively applied in magnetic and spintronic devices using ferrimagnetic Mn4N films, because Hc is an important determinant of the thermal stability of magnetization and working power consumption. Keywords Coercive field, Dislocation, Microstructure, Mn4N
I. Introduction Uniaxial magnetic anisotropy energy density (Ku) and saturation magnetization (Ms) for magnetic thin films are responsible for the efficiency of current-induced magnetization switching in recent spintronic applications such as magnetic random access memories,1–4 in which various magnetic thin films have been employed. In particular, for Mn-based nitride thin films with antiperovskite structure, several magnetic structures have been revealed to date, which are non-collinear antiferromagnetism for Mn3XN (X: transition metals)5,6 and collinear ferrimagnetism for 001-oriented 3 Mn4N films with perpendicular magnetic anisotropy (PMA).7–12 In contrast to these films, the dominant magnetic structures for the different 111-oriented Mn4N films are non-collinear,13–17 and the possible magnetic compensation and related phenomena are studied in MnXN thin films.18–21 These magnetic structures are strongly affected by the atomic-site ordering of N at the body-centered site (S) in the antiperovskite unit cell; therefore, PMA for the 001-oriented Mn4N films with a magnetic easy axis pointing perpendicular to the film plane suppressed in the case of S far from the maximum value.11,12 This may be applicable to alloy thin films with PMA such as FePt,22 MnAl,23 and MnGa.24 However, we have also found an additional issue from the previous study that non-negligible deviation of coercive field (Hc) is observed in the 001-oriented Mn4N films regardless of the S near maximum values in the experiments.25 In addition, some reports show the different size of Hc depending on the substrates and fabrication techniques, such as molecular beam epitaxy and sputtering.10,11,26 Although the mechanisms of various Hc are extensively investigated in numerous bulks and thin films to date except for the Mn4N films,27–31 there has been no focus on which factors contribute to Hc sensitively, in the case of specific Mn4N thin films. Understanding the variation of Hc in the Mn4N ferrimagnetic thin films with maximum S leads to an efficient tunability of Hc, which is indispensable for Mn4N films to realize advanced spintronic devices. For example, the enhanced Hc can provide thermal stability without bias fields, resulting in a reliable thermal-flux sensor based on the anomalous Nernst effect,32 and the suppression of Hc can 4 reduce the magnetic switching barrier, resulting in a low critical current density for magnetic memory.1–4 In addition, skyrmion bubbles and their related topological Hall effects are observed in Mn4N films,33–37 such that the Hc fine-control technology can realize future skyrmionic quantum storage systems.38 The present study aims to identify the key factors that determine the deviation of Hc for 001-oriented Mn4N films with maximum S. Three Mn4N films were prepared at three different substrate temperatures (Tsub), all of which have almost the same S. Structural analysis and the magnetic and transport properties of the films were examined. As a result, Hc was sensitive to grain diameter, microstructure, and strain, which were not detectable by X-ray diffractometry (XRD). Finally, we discuss technology for controlling Hc in ferrimagnetic Mn4N films. II. Experimental procedures Thin films of 25-nm-thick Mn4N were deposited on a single-crystal 100-MgO substrate via reactive nitridation sputtering. Three Tsub were employed: 400, 450, and 500 °C. The flow rate of N2 to Ar gas were in the ratio of 16%. Structural analysis was performed using XRD with Cu K radiation (SmartLab, Rigaku Corporation, Tokyo, Japan) and transmission electron microscopy (TEM) (Titan G2 80-200, FEI Company (Thermo Fisher Scientific), Oregon, USA). The surface roughness (Ra) and morphology were observed via atomic force microscopy (AFM) (SPA400, SII Nano Technology Inc., Tokyo, Japan). Magnetic properties were measured using a vibrating sample 5 magnetometer (VSM; VSM 8600 series, Lake Shore Cryotronics, Inc., Ohio, USA) at room temperature. The Ku was determined using the saturation torque amplitudes, where the external magnetic field rotates out-of-plane.39 III. Results and discussions A. Characterization of Mn4N crystal structures Figure 1(a) shows the out-of-plane XRD profiles of the Mn4N films fabricated at Tsub values of 400, 450, and 500 C (red, black, and blue, respectively). The peaks at 2 ≈ 23 and 47 indicate diffraction from Mn4N 001 and 002, respectively. Such diffraction angles were consistent for the three samples, suggesting no significant change in the out-of-plane lattice constant, regardless of the different Tsub. These results were applicable to in-plane XRD, as shown in Fig. 1(b); that is, the in-plane lattice constants were independent of Tsub. The Mn-O indicates natural oxidation layers because the diffraction peaks of Mn-O at 2 ≈ 41 were predominant for the in-plane XRD compared with those for the out-of-plane XRD, and the presence of Mn-O natural oxidation layer has been identified by our previous study with cross-sectional TEM observation.12 The inset of Fig. 1(c) represents the Mn4N unit cell, in which the directions of magnetic moments alternate along the [001] direction, resulting in the ferrimagnetic order with PMA.12 The c/a was estimated to be ~0.989 for all samples, which is the typical value for Mn4N films with sizable PMA.10–12 Judging from the results that no diffraction peaks were observed in the grazing incidence XRD, the present Mn4N films formed a strong 6 (001) fiber sheet texture without any polycrystals. The full-width at half-maximum of the rocking curves (1/2) showed similar values for all samples, suggesting that the deviation in the crystal orientation was comparable for all samples or slightly increased with increasing Tsub [Fig. 1(d)]. These results show that the variation in crystal structures depending on Tsub was not clearly detected by XRD analysis. B. Non-negligible coercivity deviation for Mn4N films Figure 2(a) shows the M-H (magnetization - field) hysteresis loops for the Mn4N films fabricated with three different Tsub. The Ms was similar for the three samples, as shown in Fig. 2(b), whereas the non-negligible variation of Hc was evident: Hc ≈ 10 kOe (7.5 kOe) for Tsub = 400 C (500 C), that is, Hc was suppressed by higher Tsub. Figure 2(c) shows the Ku for three samples measured via the anomalous Hall effects while rotating the external field in the yz-plane, as shown in the inset,39 The coherent magnetization rotation model being considered, Hc should be comparable to the anisotropy field (Hk), which is expressed as Hc ≈ Hk = 2Ku/Ms; therefore, the deviation of Hc observed in this study cannot be explained by either Ku or Ms. To address this point quantitatively, the measured Hc for the three samples was compared with the Hk (estimated by 2Ku/Ms using the measured Ku and Ms) [Fig. 2(d)]. As a result, the Hc was smaller by ~40% (~60%) for Tsub = 400 C (500 C) than Hk. These results can be explained by the domain nucleation mechanism prior to coherent rotation. Figure 2(d) also shows the variation in Hc and Hk normalized by those for Tsub = 400 C. More 7 importantly, the decrease in Hc by 26% was more tangible compared with the decrease in Hk by 4% with increasing Tsub, suggesting the superposition of different suppression mechanisms from the domain nucleation. To explore the possible mechanisms that cause such suppression of Hc with increasing Tsub, the three samples were systematically investigated in terms of the crystal microstructure, morphology, and transport properties. C. Grain diameter and strain estimated from XRD profiles Figure 3(a) shows the in-plane grain diameter (Dgrain) estimated using Scherrer’s formula:40 D = K/cos, where the constant K = 0.94 was employed because the diffraction peak from Mn4N 200 was fitted by a Gaussian function,  is the wavelength of Cu K radiation (0.154 nm),  is the full width at half maximum of the peak, and  is the diffraction angle of Mn4N 200 in the in-plane XRD profiles [Fig. 1(b)]. Although the difference was not significant, an increase in Dgrain was evident with increasing Tsub, suggesting grain growth of Mn4N with increasing Tsub, as confirmed in the AFM images [see insets of Fig. 3(a)]. The Ra also increased with increasing Tsub, which can be attributed to the grain growth of Mn4N. This may be due to the nature of the metallic films fabricated at high Tsub values. In addition to the trend of Dgrain, Fig. 3(b) shows the strain () estimated using the formula  = /4tan. The largest  of ~0.465% was obtained for Tsub = 400 C, suggesting the tensile strain, which decreased with increasing Tsub. Although the Tsub-dependent variation of  was approximately 5% of the  for Tsub = 400 C, the variation should be accounted for as a candidate to affect Hc, in terms of 8 the prediction that strain gives rise to a significant magnetic frustration in the Mn-based antiperovskite nitrides such as Mn3XN.41 D. Undetectable microstructures via XRD Figure 4(a1) shows a cross-sectional annular dark-field scanning transmission electron microscopy (ADF-STEM) image of the Mn4N film fabricated at Tsub = 400 C, with the largest Hc of 10 kOe. The inset shows a representative electron diffraction pattern for a large part of the Mn4N film, that is, the diffraction pattern does not indicate the local but the averaged (corresponding to the area with 10 m width of this STEM image) crystal structures. The appearance of inhomogeneous contrast in the STEM image was consistent with the previous report of Mn4N films fabricated using a facing-target sputtering technique.42 Such nonuniform microstructures are widely known as Moire fringes that appear when two or more crystal lattices are interfered with.43 Therefore, it is inferred that the present Mn4N film may involve grains with both tiny lattice distortions and rotations. The diffraction pattern exhibited clear spots originating from the 002 fundamental lattice and 001 superlattice, which is consistent with the XRD profiles [Figs. 1(a) and 1(b)]. These characteristics were also observed for Tsub = 450 C and 500 C [Figs. 4(b1) and 4(c1)], that is, both STEM images exhibited inhomogeneous contrast, and the diffraction patterns exhibited clear spots originating from the 002 fundamental lattice and 001 superlattice. To explore the possible microstructure mechanisms, we studied high-resolution STEM images 9 [Fig. 4(a2)]. The substrate/film interface is depicted by a yellow dashed line. A flat and smooth layer with uniform contrast can be seen near the interface, suggesting coherent growth of the initial two or three monolayers of Mn4N. Figure 4(a3) shows the Fourier-filtered STEM image in Fig. 4(a2). Dislocations were observed on the top of the initial growth layer. They play a role in relaxing the substrate-induced stress because the in-plane lattice mismatch was larger by as much as 10% between MgO and Mn4N.44 Note that the dislocation sites agreed with those with bright contrast, which originates from the Moire fringe mentioned above, in the high-resolution STEM image, as indicated by arrows with the same length in both Figs. 4(a2) and 4(a3). These results show that the dislocations nucleate predominantly where the Mn4N grains are adjacent to those with different lattice constants and directions. Except for the in-plane dislocation near the substrate/film interface, no dislocations were observed at the middle level of the film, although an inhomogeneous contrast was still observed in the corresponding part of the film [Fig. 4(a2)]. This may be because the strain may not be too strong to nucleate any dislocations. This growth mode is reasonable in the films with mismatches as large as 10%, and we reported the same nature in the Fe4N film on a MgO substrate, the same family of antiperovskite nitrides as Mn4N.44 In contrast to the film with Tsub = 400 C, the microstructures exhibited a remarkable change at higher Tsub values. Figures 4(b2) and 4(b3) show the high-resolution STEM image and Fourier-filtered STEM image for Tsub = 450 C. Whereas the Moire fringe was still observed [Fig. 4(b2)], as 10 in the case for Tsub = 400 C, many dislocations nucleated at sites far from the substrate compared with those near the substrate/film interface [Fig. 4(b3)]. Possible interpretations to be considered are: Larger strain could be expected compared with the case of lower Tsub, considering the thermal expansion coefficient of MgO;45 such strain was introduced up to the middle level of the film with less dislocations owing to the thermal effect, followed by nucleation of dislocation remarkably occurred, which was never found in the film for Tsub = 400 C. These results were applicable for the case of Tsub = 500 C [Figs. 4(c2) and 4(c3)], that is, overall, the microstructures for Tsub = 500 C can be explained by a scenario similar to those for Tsub = 450 C. This feature might be in agreement with the non-linear variation of Dgrain, , and even magnetic properties against Tsub: A large (relatively small) variation was observed at Tsub between 400–450 C (450–500 C) (Figs. 3). E. Influences on the longitudinal and transverse resistivity To study the effect of Tsub on the electron transport properties, we measured both the longitudinal (xx) and transverse resistivity (xy) of Mn4N films fabricated with three different Tsub. Figures 5(a) and 5(b) show xx and xy, respectively, as a function of the measurement temperature (T). Consistent with previous results, both xx and xy decreased with decreasing T.37 The film for Tsub = 400 C showed a slightly smaller value compared with the other two samples. We consider that such a small discrepancy can be ignored, which is supported by the relationship between the transverse (xy) and longitudinal conductivity (xx), that is, the three films agree with each other [Fig. 5(c)]. Because 11 the xy showed almost constant values at approximately xx ≈ 104 S/cm, it was inferred that the xy for the films could be dominated by an intrinsic rather than extrinsic origin.46 Figure 5(d) shows the dependences of 0xx and 0xy on Tsub at 5 K, which corresponds to the values eliminating the contributions from phonons. Clear Tsub dependences cannot be observed for either value, suggesting that the different microstructures of the three Mn4N films did not play a significant role in varying the transport properties. To discuss the dominant influential factors on Hc in the case of ferrimagnetic Mn4N films with the maximum S, experimental data were replotted against Hc, as shown in Fig. 6. We categorized these results into four contribution types: the averaged crystal structure evaluated via XRD [Figs. 6(a) and 6(b)], surface roughness [Fig. 6(c)], microstructure [Figs. 6(d) and 6(e)], and transport properties [Fig. 6(f)]. As a result, it was revealed that the S, 1/2, and electronic transport properties do not significantly contribute to Hc, whereas the surface roughness and microstructure are the keys to modulating Hc in ferrimagnetic Mn4N films. Therefore, we have eliminated the S, 1/2, and electronic transport properties from our discussion. A small Dgrain was responsible for the decreased Ra, resulting in the enhancement of Hc. To understand this point first, we consider the Stoner-Wohlfarth model without magnetic interaction, given by the following formula:30 𝐻𝑐 = 0.4822𝐾𝑢𝜇0𝑀𝑠 = 0.482 (2𝐾1𝜇0𝑀𝑠+1−3𝑁2𝑀𝑠) , (1) 12 where Ku, 0, Ms, K1, and N represent the uniaxial magnetic anisotropy energy density, vacuum permeability, saturation magnetization, magnetocrystalline anisotropy energy density, and demagnetization factor, respectively, ranging from 0 to 1. Because K1 and Ms were independent of Tsub, judging from our experiments (Fig. 2), one of the factors that gives a different Hc is the N in the film. Therefore, Eq. (1) suggests that the enhancement of Hc can be qualitatively understood by the decrease in N when Dgrain decreases with a lower Tsub. Although the realistic value of N for each Mn4N film is still unknown in this study, this trend is consistent with the statement by Liu et al. that the local demagnetization factor decreases as the grain size is decreased.31 However, the contribution from the demagnetization factor [the second term of Eq. (1)] is not large enough to explain the variation in measured Hc with 26% against Tsub [Fig. 2(d)] because the variation in estimated Hc is only 10% with N = 0 and 1. Next, we consider  to have an additional effect on Hc. Stress-induced enhancement of Hc by 300% was demonstrated in a ferrimagnetic amorphous TbFeCo thin film with PMA by Anuniwat et al.28 In the case of Mn4N films, it was revealed that the number of dislocations was enhanced with higher Tsub (Fig. 4), resulting in the suppression of  with higher Tsub [Fig. 3(b)]. Therefore, the enhancement of Hc in Mn4N films with a lower Tsub is also associated with the enhancement of . These results lead us to conclude that the variation in the measured Hc depending on Tsub in the Mn4N films could be dominantly affected by the combined classical mechanisms of ferromagnets and/or ferrimagnets, which are demagnetization factors determined by the grain size and the effective residual 13 strain with dislocations. The Hc for the optimum Mn4N films with the maximum S was found to be sensitive to the grain size and strain as a result of a specific substrate temperature. Such tunable Hc is an attractive phenomenon from the perspective of magnetic and spintronic devices: Thermal stability can be improved by a large Hc without bias fields and reduction of working power consumption by a small Hc. In addition, the size of skyrmion bubbles can be manipulated without a bias field. The technology to tune Hc could thus promote Mn4N based spintronic devices in the future. IV. Conclusion It is already known that the Hc of Mn4N ferrimagnetic thin films is strongly governed by their degree of order of N. This is due to the strong correlation between the degree of order of N and PMA. Namely, the out-of-optimization content of N as well as Tsub causes less degree of order of N and decrease in PMA, resulting in small Hc, which might be general characteristics for magnetic nitrides. However, this study specifically focused on the property of Hc that could be modulated by dislocations as well as microstructures with similar S, which has not previously been examined in detail via TEM observation. Neither the deviation of crystal orientation nor the longitudinal and transverse resistivity contribute significantly to Hc; however, it is sensitive to the demagnetization factor, determined by the grain size and the effective residual strain with dislocations. This type of tunability of Hc is an intriguing characteristic of Mn4N films with a maximum degree of order of N. 14 The results demonstrate that decreasing or increasing the grain size and number of dislocations via optimization of the substrate temperature and/or lattice mismatch between the substrate and film is a promising method to enhance or suppress Hc. This work was supported by KAKENHI Grants-in-Aid (Nos. 18H03787 and 19K04499) from the Japan Society for the Promotion of Science (JSPS). Part of this work was carried out under the Cooperative Research Project Program of RIEC, Tohoku University. The data supporting the findings of this study are available from the corresponding author upon reasonable request. The authors have no conflict of interests to declare. 15 [1] C. Slonczcwski, J. Magn. Magn. Mater. 159, L1 (1996). [2] L. Berger, J. Appl. Phys. 55, 1954 (1984). [3] R. H. Koch, J. A. Katine, and J. Z. Sun, Phys. Rev. Lett. 92, 088302 (2004). [4] S. Ikeda, K. Miura, H. Yamamoto, K. Mizunuma, H. D. Gan, M. Endo, S. Kanai, J. Hayakawa, F. Matsukura, and H. Ohno, Nature Mater. 9, 721 (2010). [5] X. Zhou, J.-P. Hanke, W. Feng, F. Li, G.-Y. Guo, Y. Yao, S. Blügel, and Y. Mokrousov, Phys. Rev. B 99, 104428 (2019). [6] V. T. N. Huyen, M. Suzuki, K. Yamauchi, and T. Oguchi, Phys. Rev. B 100, 094426 (2019). [7] W. J. Takei, G. Shirane, and B. C. Frazer, Phys. Rev. 119, 1893 (1960). [8] W. J. Takei, R. R. Heikes, and G. Shirane, Phys. Rev. 125, 1893 (1962). [9] K. M. Ching, W. D. Chang, T. S. Chin, J. G. Duh, and H. C. Ku, J. Appl. Phys. 76, 6582 (1994). [10] Y. Yasutomi, K. Ito, T. Sanai, K. Toko, and T. Suemasu, J. Appl. Phys. 115, 17A935 (2014). [11] K. Kabara, and M. Tsunoda, J. Appl. Phys. 117, 17B512 (2015). 16 [12] S. Isogami, K. Masuda, and Y. Miura, Phys. Rev. Mater. 4, 014406 (2020). [13] M. Uhl, S. Matar, and P. Mohn, Phys. Rev. B 55, 2995 (1997). [14] S. Dhar, O. Brandt, and K. H. Ploog, Appl. Phys. Lett. 86, 112504 (2005). [15] Z. Zhang, Y. Cho, J. Singhal, X. Li, P. Dang, H. Lee, J. Casamento, Y. Tang, H. G. Xing, and D. Jena, AIP Adv. 10, 015238 (2020). [16] Z. Zhang, Y. Cho, M. Gong, S.-T. Ho, J. Singhal, J. Encomendero, X. Li, H. Lee, H. G. Xing, and D. Jena, IEEE Trans. Magn. 58, 2400106 (2021). [17] S. Isogami, N. Rajamanickam, Y. Kozuka, and Y. K. Takahashi, AIP Adv. 11, 105314 (2021). [18] S. Isogami, A. Anzai, T. Gushi, T. Komori, and T. Suemasu, Jpn. J. Appl. Phys. 57, 120305 (2018). [19] T. Komori, T. Gushi, A. Anzai, L. Vila, J.-P. Attane, S. Pizzini, J. Vogel, S. Isogami, K. Toko, and T. Suemasu, J. Appl. Phys. 125, 213902 (2019). [20] H. Mitarai, T. Komori, T. Hirose, K. Ito, S. Ghosh, S. Honda, K. Toko, L. Vila, J.-P. Attané, K. Amemiya, and T. Suemasu, Phys. Rev. Mater. 4, 094401 (2020). 17 [21] T. Komori, T. Hirose, T. Gushi, K. Toko, T. Hanashima, L. Vila, J.-P. Attane, K. Amemiya, and T. Suemasu, J. Appl. Phys. 127, 043903 (2020). [22] M. R. Visokaya, and R. Sinclair, Appl. Phys. Lett. 66, 1692 (1995). [23] T. Sands, J. P. Harbison, M. L. Leadbeater, S. J. Allen, Jr., G. W. Hull, R. Ramesh, and V. G. Keramidas, Appl. Phys. Lett. 57, 2609 (1990). [24] H. Kurt, K. Rode, M. Venkatesan, P. Stamenov, and J. M. D. Coey, Phys. Rev. B 83, 020405(R) (2011). [25] S. Isogami, K. Masuda, Y. Miura, N. Rajamanickam, and Y. Sakuraba, Appl. Phys. Lett. 118, 092407 (2021). [26] T Gushi, L. Vila, O. Fruchart, A. Marty, S. Pizzini, J. Vogel, F. Takata, A. Anzai1, K. Toko, T. Suemasu, and J.-P. Attané, Jpn. J. Appl. Phys. 57, 120310 (2018). [27] W. B. Cui, Y. K. Takahashi, K. Hono, Acta Mater. 59, 7768 (2011). [28] N. Anuniwat, M. Ding, S. J. Poon, S. A. Wolf, and J. Lu, J. Appl. Phys. 113, 043905 (2013). [29] H. Sepehri-Amin, T. Phkubo, M. Gruber, T. Schrefl, and K. Hono, Scripta Mater. 89, 29 (2014). 18 [30] Y. Takahashi, T. Kadono, S. Yamamoto, V. R. Singh, V. K. Verma, K. Ishigami, G. Shibata, T. Harano, Y. Takeda, T. Okane, Y. Saitoh, H. Yamagami, M. Takano, and A. Fujimori, Phys. Rev. B 90, 024423 (2014). [31] J. Liu, H. Sepehri-Amin, T. Ohkubo, K. Hioki, A. Hattori, T. Schrefl, and K. Hono, Acta Mater. 82, 336 (2015). [32] W. Zhou and Y. Sakuraba, Appl. Phys. Express 13, 043001 (2020). [33] G. Wang, S. Wu, W. Zhou, H. Li, D. Li, T. Dai, S. Kang, S. Dang, X. Ma, P. Hu, and S. Li, Appl. Phys. Lett. 113, 144403 (2018). [34] M. Meng, S. Li, M. Saghayezhian, E. W. Plummer, and R. Jin, Appl. Phys. Lett. 112, 132402 (2018). [35] C. Ma, T. Hartnett, W. Zhou, P. Balachandran, and S. Poon, Appl. Phys. Lett. 119, 192406 (2021). [36] T. Bayaraa, C. Xu, and L. Bellaiche, Phys. Rev. Lett. 127, 217204 (2021). [37] S. Isogami, M. Ohtake, and Y. K. Takahashi, J. Appl. Phys. 131, 073904 (2022). 19 [38] S. Luo, and L. You, APL Mater. 9, 050901 (2021). [39] T. Ono, N. Kikuchi, S. Okamoto, O. Kitakami, and T. Shimatsu, Appl. Phys. Express 11, 033002 (2018). [40] Scherrer, P., Nachr. Ges. Wiss. Göttingen, 26, 98 (1918). [41] J. Zemen, E. Mendive-Tapia, Z. Gercsi, R. Banerjee, J. B. Staunton, and K. G. Sandeman, Phys. Rev. B 95, 184438 (2017). [42] Z. Zhang, X. Shi, X. Liu, X. Chen, and W. Mi, J. Phys.: Condens. Mater. 34, 065802 (2022). [43] Q. H. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyashita, Nanotechnology 28, 455704 (2017). [44] I. Suzuki, J. Uzuhashi, T. Ohkubo, and S. Isogami, Mater. Res. Express 6, 106446 (2019). [45] M. A. Durand, Physics, 7, 297 (1936). [46] S. Onoda, N. Sugimoto, and N. Nagaosa, Phys. Rev. B 77, 165103 (2008). 20
Figure 1. (a) Out-of-plane, (b) in-plane, and (c) grazing incidence x-ray diffraction (XRD) profiles for the Mn4N films fabricated with the substrate temperature (Tsub) of 400 C (red), 450 C (black), and 500 C (blue). Inset of Fig. 1(c) represents the Mn4N unit cell with collinear ferrimagnetic magnetic structure. (d) Full-width at half-maximum value (1/2) as a function of Tsub, where 1/2 was estimated from the rocking curves of XRD as shown in the inset. Figure 2. (a) Magnetization-field (M-H) hysteresis loops for the Mn4N films fabricated with the substrate temperature (Tsub) of 400 C (red), 450 C (black), and 500 C (blue). (b) Tsub dependence of saturation magnetization (Ms), (c) uniaxial magnetic anisotropy energy density (Ku) that is estimated from the angular dependence of anomalous Hall effect, and (d) coercive field (Hc) and anisotropy field (Hk = 2Ku/Ms). Figure 3. (a) Tsub dependence of the in-plane grain diameter (Dgrain) and (b) residual strain () evaluated using XRD profiles. Surface morphologies observed via atomic force microscopy (AFM) are shown in the insets. 21 Figure 4. (a1) Cross sectional annular dark-field scanning transmission electron microscopy (ADF-STEM) image, (a2) enlarged ADF-STEM image, and (a3) Fourie filtered image for the Mn4N film fabricated with the substrate temperature (Tsub) of 400 C. The inset represents the electron diffraction patterns for the Mn4N film. (b) and (c) show the same set of images as (a) with the Tsub of 450 C and 500 C, respectively. Figure 5. (a) Measurement temperature dependence of longitudinal resistivity (xx) and (b) transverse resistivity (xy) for the Mn4N films fabricated with the substrate temperature (Tsub) of 400 C (red), 450 C (black), and 500 C (blue). (c) Relationship between transverse conductivity (xy) and longitudinal conductivity (xx). (d) Tsub dependence of residual resistivity (0xx) and residual transverse conductivity (0xy). Figure 6. Replot of various measurement data against coercive field (Hc). 22 Fig. 1 400 450 5000.911.11.21.3Tsub. (℃)1/2 (deg.)20 30 40 50 602   (deg.)Log intensity (arb. unit)20 30 40 50 602   (deg.)Log intensity (cps)20 30 40 50 602 (deg.)Log intensity (cps)  = 1°20 22 24 2605001000 (deg.)Linear intensity (a.u.)400℃450℃500℃*▲*▲* MgO sub.▼ MnO(a) (b)(c)Mn4N 002Mn4N 001Mn4N 200Mn4N 100(d)==1/2 = 1°Tsub23 Fig. 2 400 450 5001234Tsub. (℃)Ku (M erg/cm3)(a) (b)0 45 90 135 180-2-1012[106]M (deg.)T (dyne cm)(c) (d)HcHkHcHkMxzy400 450 50090100110Tsub. (℃)Ms (emu/cm3)400 450 500691215180.51Tsub. (℃)Hc, Hk (kOe)Normalized Hc, Hk (a. u.)-10 0 10-1000100Hz (kOe)M (emu/cm3) Tsub 500 ℃ 450 ℃ 400 ℃24 Fig. 3 (a) (b)200 nm 200 nm 200 nmRa : 3.1Å 5.2Å 6.4Å400 450 50018192021Tsub. (℃)Dgrain (nm)400 450 5004.34.44.54.64.7Tsub. (℃) (×10-3)25 Fig. 4 (c1)(b1)(a1)Mn-OMn4NMgO sub.0010010020020005 nm5 nm5 nm(c2)(b2)(a2)(c3)(b3)(a3)Mn-OMn4NMgO sub.Mn-OMn4NMgO sub.Mn4NMgO sub.Mn4NMgO sub.Mn4NMgO sub.10 nm10 nm10 nm400 ℃450 ℃500 ℃26 Fig. 5 103 104 105101102xx (S/cm)|xy| (S/cm)(a) (b)(c) (d)5 K300 K5 K0 100 200 300100200300T (K)xx ( cm) Tsub. 400℃ 450℃ 500℃0 100 200 30001234T (K)xy ( cm)400 450 500607080905060708090Tsub (℃)0xx ( cm)|0xy| (S/cm)27 Fig. 6 7 8 9 100.80.850.90.95S7 8 9 1011.11.21.31.41.51/2 (deg.)7 8 9 1000.20.40.60.81Ra (nm)(a) (b) (c)(d)Coercive field, Hc (kOe)(e) (f)7 8 9 106070809050607080900xx ( cm)|0xy| (S/cm)7 8 9 10192021Dgrain (nm)7 8 9 104.34.44.54.64.7Strain (×10-3)