Journal of Magnetism and Magnetic Materials 495 (2020) 165873
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Research articles
Synergistic effect of lattice strain and Co doping on enhancing thermal stability in Fe16N2 thin film with high magnetization
T
⁎
Lei Wanga, Chun Fenga, , Mi-Dan Caoa, Fei Menga, Yu-Kun Lia, Jian-Juan Yina, Bao-He Lib, ⁎ ⁎ Shigenobu Ogatac,d, Wen-Tong Genga,c, , Guang-Hua Yua, a
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China Department of Physics, School of Sciences, Beijing Technology and Business University, Beijing 100048, China c Department of Mechanical Science and Bioengineering, Osaka University, Osaka 5608531, Japan d Center for Elements Strategy Initiative for Structural Materials, Kyoto University, Kyoto 606-8501, Japan b
A R T I C LE I N FO
A B S T R A C T
Keywords: FeN alloy film Magnetism Thermostability Lattice strain Atomic substitution
Single phase Fe16N2 is a potential material in building high-performance magnetic writing heads and permanent magnets due to its ultra-high saturation magnetization (MS) and magnetic anisotropy (Keff). However, the poor controllability of phase constituent and low thermostability (decomposed at 200 °C) are big obstacles to its practical applications. In this work, we have devised a novel Fe/Cr/FeN:Co heterostructure to introduce both lattice strain and Co doping for tuning the FeN constituent and enhancing the phase stability synergistically. With effective regulation, the FeN layer can possesse both superior MS (2.4–2.8 T) and high thermostability with standing 450 °C annealing. Furthermore, by first-principles calculations, we reveal that the synergistic regulation on the thermostability is closely related to the solution heat tunability of Fe-N phases. The Fe/Cr/FeN:Co heterostructure may serve as a promising material for constructing high-efficient writing heads, permanent magnets, and other magnetic devices.
1. Introduction Ferromagnetic materials with high saturation magnetization (MS) and good thermostability are desirable for constructing high-performance magnetic writing heads and permanent magnets [1–8]. α″Fe16N2 single phase, constituted by ordered filling N atoms into bodycentered-cubic Fe interstitial sites, was predicted to bear giant MS of 2.9 T and large magnetocrystalline anisotropy (Ku) of 106 J/m3 [9–11]. These advantages make the material become a potential candidate of writing head material and permanent magnets. However, the α″-Fe16N2 material has never been developed in practical application, which is severely restricted by unsteerable phase constituent and poor thermostability for 60 years. The Fe16N2 phase is thermodynamically unfavorable due to a large formation enthalpy of 85 kJ/mol [12], resulting in a difficulty in generating single Fe16N2 phase to obtain the superior performance in an actual film. Although many researchers attempted to enhance the Fe16N2 phase by expanding cell volume to accommodate more N atoms [13–17], the achievable magnetic properties are still not high and readily tunable. Thus, it is desirable to increase the fraction of Fe16N2 phase in a film. Moreover, the dissolved N atoms are easy to diffuse at a low temperature of 200 °C, leading to a Fe16N2 phase ⁎
decomposition [12,18]. In order to suppress the N diffusion and stabilize the Fe16N2 phase, doping impurity elements (Mn, Ti, Al etc.) [19–22] was proposed, which however leads to nonnegligible magnetism decrement. So far, it is difficult to achieve a FeN film with both superior magnetism and high thermostability. In our previous work, we used a Cr buffer layer to promote the Fe16N2 formation in a FeN film by decreasing activation energy for the phase transition from Fe8N to Fe16N2, which leads to a considerable increment of magnetization [23]. However, the film still shows a poor thermostability, which will restrict the real performance and device applications in the future. Now the research interest is whether we can use a more effective crystal regulation to tackle the challenge. In this work, we devised a novel Fe/Cr/FeN:Co heterostructure to introduce both biaxial (0 0 1) in-plane tensile strain and Co atomic substitution for synergistically tuning FeN crystal lattice. Under such effect, the FeN phase constituent was well-controlled with an apparent increment of Fe16N2 phase, which brings about tunable magnetism with the MS ranging 2.4–2.8 T. Meanwhile, the Fe16N2 phase was stabilized by modulating the solution heat of FeN phases, enabling the heterostructure good thermostability with an enhanced thermotolerance temperature from 200 to 450 °C.
Corresponding authors at: School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China (C. Feng). E-mail addresses:
[email protected] (C. Feng),
[email protected] (W.-T. Geng),
[email protected] (G.-H. Yu).
https://doi.org/10.1016/j.jmmm.2019.165873 Received 22 April 2019; Received in revised form 17 September 2019; Accepted 17 September 2019 Available online 17 September 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 495 (2020) 165873
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2. Experiment
compared with the strain-free Fe-buffer-sample, Cr (or Pt) buffer layer causes an obvious Fe8N (0 0 2) peak shift towards higher (smaller) angle direction and an (2 2 0) peak shift towards smaller (higher) angle direction, implying the Cr (or Pt) buffer layer induces an in-plane tensile (compressive) strain on (0 0 1) plane of the as-deposited Fe8N layer. Based on the Fe8N (2 2 0) peak shift with the reference of Fe-buffersample, the lattice strain can be calculated, as shown in Table 1. After 180 °C annealing to the Pt-buffer-sample, the Fe8N (0 0 2) peak is greatly weakened, accompanying with emergence of Fe4N (2 0 0) peak and strengthening of Fe (0 0 2) peak (Fig. 1c), demonstrating that the compressive strain promotes a phase transition from Fe8N to Fe4N (i.e. N occupancy site evolution from octahedral to tetrahedral). On the contrary, an apparent characteristic Fe16N2 (0 0 2) peak appears in the annealed Cr-buffer-sample, indicating that the tensile strain is favorable for the expected phase transition from Fe8N to Fe16N2 (i.e. N occupancy manner evolution from disorder to ordered one in the same interstitial site). In other words, the in-plane tensile strain is beneficial for N ordering occupancy in Fe lattice, which is related to a decreased activation energy for N atomic migration, as explained in our previous work [23]. Next, we will focus on the influence of strain on magnetic characteristics of the FeN layer. Fig. 1d shows the in-plane hysteresis loops of post-annealed samples with three buffer layers. To obtain accurate magnetization values, the real respective thicknesses of Fe and FeN layers were determined precisely by fitting X-ray reflectivity (XRR) spectra in advance. Then, with an assumption of MS-Fe = 2.1 T, MS of the FeN layer was calculated by extracting magnetic moment of the Fe seed layer from overall magnetic moment of the whole sample, as shown in Fig. 1e. The remanence ratio (Mr/MS) of whole heterostructure is also summarized in Fig. 1e to demonstrate the evolution of out-of-plane magnetization component. As we mentioned before, the compressive strain induced by the Pt buffer layer restricts Fe16N2 phase, thus, the FeN layer shows a low MS = 2.11 T. Besides, an apparent easy magnetization characteristic with a high remanence ratio of 0.81 is observed in Fig. 1d, implying in-plane magnetic anisotropy (IMA) is developed in both the FeN and Fe layers. However, Cr-buffer-sample displays an apparent two-step magnetization reversal behavior in Fig. 1d. The steep reversal at a low field stems from Fe seed layer with an in-plane anisotropy. As in-plane field increases beyond 300 Oe, the loop shows a typical hard magnetization behavior with a noticeable inplane saturation field of 6.6 kOe and a remarkable decrease of remanence ratio to 0.38. This result indicates that a strong magnetocrystalline anisotropy (MCA) is developed in the FeN layer which favors the alignment of easy-axis perpendicular to film plane. Quantitatively, the magnetic anisotropy energy in FeN layer (KFeN) is calculated to be 0.7 × 106 J/m3 with using a formula of KFeN = MS × HK-FeN/2, where the anisotropy field of FeN layer (HK-FeN) is roughly estimated by using the intersection of in-plane and out-of-plane loops. The high MCA in the FeN layer, accompanying with an obvious MS increment to 2.45 T, derives from the promotion of Fe16N2 phase by the tensile strain. In order to optimize the strain effect, the MS variation with FeN thickness (dFeN) was studied. Due to a stress relaxation along FeN thickness direction, the aforementioned strain effect is strongly related to dFeN. As the FeN layer becomes thinner, the effective strain on whole FeN layer is gradually enhanced, leading to an ultrahigh MS = 2.81 T (30%
2.1. Sample preparations Two types of samples were prepared on MgO (0 0 1) single crystal substrates by magnetron sputtering. I) Samples without Co doping: Fe (10)/X(5)/FeN(dFeN)/Cr(3) with the buffer layer X = Cr, Fe, or Pt, and an FeN layer thickness (dFeN) of 5–50 nm. II) Co doped samples: Fe(10)/ Cr(5)/(Fe1-yCoy)N(10)/Cr(3), where the nominal Co concentration (y) was in a range of 0–30.0 at.%, calculated from the deposition rate ratio of Fe to Co targets. The units of all layer thicknesses are in nm. All the samples were prepared in a vacuum chamber with a base pressure lower than 5 × 10−5 Pa. The Fe seed layer was deposited at 200 °C for a better (0 0 1) epitaxial growth of the subsequent layers growing at 25 °C. The seed/buffer/cap layers were prepared at an Ar gas pressure of 0.45 Pa and the FeN or (Fe1-yCoy)N layer was deposited with thoroughly Ar and N2 gas mixture at a ratio of 21:1. Finally, the as-deposited samples were annealed at temperatures in the range of 50–550 °C in a vacuum of 3 × 10−5 Pa for 13 h. 2.2. Sample characterizations The magnetic properties of samples were measured using a physical property measurement system (PPMS) with applied magnetic fields up to 3 T. The lattice structure change in the samples was evaluated by Xray diffraction (XRD, D/max-TTR III with using Cu Kα radiation) measurements with both θ–2θ and grazing incident modes. In addition, X-ray photoelectron spectroscopy (XPS) measurements were conducted to reveal the electronic structure evolution. The XPS spectra were collected after Ar+ etching for 130 s with an etching rate of 0.2 Å/s. An Al Kα source was used as the incident radiation source, providing X-rays of energy 14.5 eV. 2.3. Theoretical computation First-principles density functional theory calculations were carried out to study the synergistic effects of lattice strain and Co substitution by using Vienna ab initio simulation package (VASP) [24]. The electronion interaction was described using the projector augmented wave method [25] and the exchange correlation potential using the generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof form [26]. 3. Results and discussion In order to study the lattice strain effects on Fe-N phase systematically, we utilized three kinds of buffer layers, namely Cr, Fe, and Pt, to introduce tensile strain, strain-free, and compressive strain on the FeN layers due to the lattice mismatch on (0 0 1) plane in Table 1. Fig. 1a-1c show the crystal structure evolution in the Fe(10)/X(5)/FeN (50)/Cr(3) samples (X = Cr, Fe, and Pt). For the as-deposited samples, strong Fe8N (0 0 2) peak emerges in the high angle XRD patterns (Fig. 1a) and clear Fe8N (2 2 0) peak appears in the grazing incident XRD patterns (Fig. 1b), implying the formation of stable α′-Fe8N phase in the as-deposited film whatever the buffer layer is. However,
Table 1 Epitaxial relationship, theoretical lattice mismatch, and experimental strain in FeN films with different buffer layers. Heterostructure
Epitaxial relationship and lattice mismatch
Experimental in-plane strain on (0 0 1) plane
Cr/FeN (50 nm)
bcc-Cr[1 0 0](0 0 1) || bct-FeN[1 0 0](0 0 1) (+1.74% mismatch) bcc-Fe[1 0 0](0 0 1)|| bct-FeN[1 0 0](0 0 1) (0.244% mismatch) fcc-Pt[1 1 0](0 0 1)|| bct-FeN[1 0 0](0 0 1) (−3.10% mismatch)
+0.61%
Fe/FeN (50 nm) Pt/FeN (50 nm)
2
— −0.78%
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Fig. 1. Lattice strain effects on phase formation and magnetic properties of Fe(10)/X(5)/FeN(50)/Cr(3) samples (X = Cr, Fe, or Pt). (a), (b) High angle and grazing incident XRD patterns of the as-prepared samples. (c), (d) High angle XRD patterns and in-plane hysteresis loops of the annealed samples. (e) MS of the FeN layer and Mr/MS of the samples with different bufferlayers. (f) MS variations of the FeN layer in the Fe(10)/Cr(5)/FeN(dFeN)/Cr(3) samples with dFeN.
annealed at different temperatures. The typical in-plane hysteresis loops for y = 0 at.%, 6.25 at.%, and 30.0 at.% are shown in Fig. 3a-3c. Fig. 3d summarizes the MS dependence of the FeN layer on TA under variable y. In the absence of doped Co atoms, MS increases with TA before reaching a maximum of 2.81 T at TA = 180 °C and then decreases below 2.4 T at TA > 250 °C. The dominant phase evolutions are Fe16N2 formation (TA < 180 °C) and Fe16N2 decomposition to other FeN phases (TA > 180 °C). The complete decomposition temperature (TD) of Fe16N2 phase is inferred as 250 °C which is comparable to the values in reported literatures [9,27,28,30]. These results reveal that TD cannot be improved effectively with the singular lattice strain effect. However, with a 6.25 at.% Co doping, MS maintains beyond 2.5 T in a broad TA range of 180–450 °C. Accordingly, the characteristic Fe 2p3/2 and Co 2p3/2 peaks in XPS spectra do not shift remarkably with low Co doping (Fig. 4a and 4b) and with increased TA (Fig. 4d and 4e), implying that Co substitutes Fe to form (Fe1-yCoy)16N2 instead of destructing the Fe16N2 structure. Meanwhile, the binding energy of N 1 s electron in Fig. 4f maintains at 397.1 eV (corresponding to Fe16N2 phase [28]) at TA ≤ 450 °C and shifts to 396.7 eV (corresponding to Fe4N phase [28]) at 550 °C. This provides a concrete evidence that doping proper amount of Co favors for well-stabilizing Fe16N2 phase and substantially enhancing thermostability with bearing 450 °C annealing, meanwhile maintaining a high MS = 2.60 T. However, with doping Co excessively (y = 16.5–30.0 at.%), the MS variation tendency with TA is totally
increment over the Fe-buffer-sample) at dFeN = 10 nm, as shown in Fig. 1f. These results tell us that the magnetism of FeN alloy can be properly-modulated using the in-plane tensile strain. Next, we turn to study the influence of strain on thermal stability. Fig. 2 plots the in-plane hysteresis loops of Fe(10)/X(5)/FeN(50)/Cr(3) samples with annealing temperatures (TA). The MS dependence on TA is summarized in Fig. 2d. As we know, an appropriate annealing can promote the formation of Fe16N2 phases, leading to a MS increment with increasing TA. However, when TA exceeds a certain value, the annealing will result in a Fe16N2 decomposition and a MS decrement. Therefore, we can evaluate the phase thermostability with the starting decomposition temperature which corresponds to the turning point of MS evolution in Fig. 2d. When the FeN layer is subjected to different lattice strain, the starting decomposition temperature changes from 100 °C (Pt-buffer-sample) to 140 °C (Fe-buffer-sample) and 180 °C (Crbuffer-sample). This result indicates that the tensile strain is beneficial for enhancing thermal stability to some extent. However, the bearable temperature is only 180 °C which is not high enough for practical applications. To improve the phase thermostability, we dope some amount of Co atoms in the FeN layer to introduce a synergistic effect of lattice strain and Co substitution. Here, 10 nm thick FeN was selected due to the optimized strain effect and superior MS. A series of Fe(10)/Cr(5)/ (Fe1-yCoy)N(10)/Cr(3) samples with various amount of Co doping were 3
Journal of Magnetism and Magnetic Materials 495 (2020) 165873
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Fig. 2. In-plane hysteresis loops of the annealed Fe (10)/X(5)/FeN (50)/Cr(3) samples with TA: (a) X = Fe; (b) X = Cr; (c) X = Pt. All insets show the enlarged loops in a field range of 0–8 kOe. (d) MS variation of the Fe (10)/X(5)/FeN (50)/Cr(3) samples with TA.
Fig. 3. Co-doping induced magnetism and thermostability tunability. (a)-(c) In-plane hysteresis loops of the annealed Fe(10)/Cr(5)/(Fe1-yCoy)N (10)/Cr(3) samples with typical TA of y = 0 at.% (a), y = 6.25 at.% (b), and y = 30.0 at.% (c). (d) MS variations of the FeN layer with TA for different y. (e) MS dependence on y at TA = 180 °C. (f) Comparison of the achievable MS and TD between our heterostructure and other reported FeN systems [9,19,20,22,31–34].
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Fig. 4. Co-doping induced electronic structure evolution. The high-resolution Fe2p, Co2p, and N1s XPS spectra in the FeN layer of Fe(10)/Cr(5)/(Fe1-yCoy)N (10)/Cr (3) with varying y at TA = 220 °C (a)-(c), and with changing TA when y = 6.25 at.% (d)-(f) and y = 30.0 at.% (g)-(i).
Fig. 5. Co-doping induced crystal structure evolution. XRD patterns of Fe(10)/Cr(5)/(Fe1-yCoy)N (10)/Cr(3) samples: (a) TA = 220 °C; (b) TA = 250 °C; (c) TA = 350 °C; (d) TA = 450 °C. All insets show the enlarged patterns in the 2θ range of 62°–68°.
to 65.2° [corresponding to CoFe(2 0 0)], as shown in the inset of Fig. 5c and 5d. Additionally, both Fe 2p3/2 and Co 2p3/2 XPS peaks move towards a higher binding energy by 0.4 eV (Fig. 4g-4 h). This result implies that elevated TA causes the superabundant Co to bond with Fe to form CoFe alloy with a much higher MS = 2.45 T [31]. Thus, a monotonical MS increment with TA is observed in Fig. 3d. So far, a FeN-based heterostructure with superior and tunable magnetism (MS ranging 2.4–2.8 T) and good thermostability
different. MS is very low (about 1.8 T) at the as-deposited state and monotonically increases with TA until approaching a maximum of 2.4 T. At a low-TA-annealing process (TA < 350 °C), Fe4N (2 0 0) peak emerges in XRD patterns (Fig. 5a and 5b) and N1s XPS peak moves to 396.7 eV (Fig. 4c), indicating that excessive Co doping destructs the Fe16N2 structure and further induces Fe4N phase with a lower MS = 1.7 T [29,30]. As TA further increases beyond 350 °C, the Fe (0 0 2) diffraction peak moves from 65.6° [corresponding to Fe(0 0 2)]
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(TD = 550 °C) is constructed through the synergistic effect of lattice strain and Co substitution (6.25 at.%). Comparing the achievable magnetism and thermal stability of our heterostructures and other reported FeN structures [9,19,20,22,31–34], we clearly see that our heterostructure occupies a unique position on the chart of MS vs. TD in Fig. 3f. The unique combination of outstanding magnetism and splendid thermostability renders the heterostructure applicable as a potential ferromagnetic material on writing heads and permanent magnets. To elucidate the underlying mechanism for the synergistic effect of lattice strain and Co substitution on thermostability tunability, we carried out first-principle calculations to determine the heat of solution for Co substituting Fe to form (Fe1-yCoy)N alloy (Es), which is defined as:
E s = E [(Fe1 − y Co y ) N ] − E (FeN ) − μCo + μFe
Table 2 The calculated structural parameters and heat of solution Es of Co in various FeN systems. Fe-N alloy
Co site
Co-N distance (Å)
Heat of solution Es (eV)
Fe4N
Fe1 Fe2 Fe1 Fe2 Fe3 Fe1 Fe2 Fe3 Fe4 Fe5
3.28 Å 1.89 Å 1.83 Å 1.95 Å 3.24 Å 3.66 Å 1.97 Å 1.78 Å 3.21 Å 4.25 Å
0.031 0.027 0.138 0.149 0.095 −0.123 0.067 0.091 −0.069 −0.055
Fe16N2
Fe16N
(1) Co substituted Fe4N system is much more stable and the Fe16N2 phase is preferred to decompose into Fe4N and Fe phases. On the contrary, if ε is higher than εc (region II), the Co atoms are preferential to stabilize Fe16N2 phase instead of Fe4N phase. This restrains the phase decomposition of Fe16N2 to Fe4N and thereby improves the thermotolerance ability. The calculated εc is about 2.5%, based on an ideal Fe16N2 cell with fully ordered N occupancy. However, only partially ordered N occupancy can be realized in a real FeN film, resulting in an occurrence of high N areas (such as Fe4N) and low N areas (such as Fe16N) at disordered occupancy regions. It is inferred from Table 2 that both areas have much smaller Es than that of ideal Fe16N2. This lowers the Es of a real Co substituted Fe16N2 system. By taking account of the ordering degree of 0.6 in our previous work [23], the εc is estimated to be about 0.5%. As shown in table 1, the achieved strain is 0.61% by choosing Cr as a bufferlayer and thick FeN thickness (50 nm). Thus, the tensile strain in thin FeN samples should be much larger than 0.61%, which leads Es fall into the region II and results in an effective improvement of thermostability. By further increasing Co concentration, the Es of Co-substituted Fe16N2 system shows a declined trend (Fig. 6c), which is more beneficial to stable the Fe16N2 phase. However, as we mentioned before, Co atoms tend to replace the farthest Fe atoms from N atoms which have weakest 3d electrons localization and largest contribution to the total magnetic moment of Fe-N cell [17]. Thus, excessive Co doping causes the rapid MS decrement in Fig. 3e. The
where E(FeN) and E[(Fe1-yCoy)N] are the total energy of FeN supercells without and with Co substitution, respectively. μCo and μFe are the chemical potential of Co and Fe in the form of elemental crystals (μFe = −8.309 eV, μCo = −7.108 eV). Firstly, we consider the low Co doping case (y = 6.25 at.%), i.e. one Fe atom in the Fe-N cell is replaced by a Co atom. Three Fe-N systems, Fe4N, Fe16N2, and Fe16N, were calculated. The Fe sites available to Co are Fe1 and Fe2 in Fe4N, Fe1, Fe2, and Fe3 in Fe16N2, Fe1, Fe2, Fe3, Fe4, and Fe5 in Fe16N, as displayed in Fig. 6a. The calculation parameters and results are shown in Table 2. The less the Es is, the more stable the Co substituted Fe-N system is. It has a very close Es value for Co substituting the Fe1 and Fe2 sites in Fe4N cell. However, it is the Fe3 site in Fe16N2 and the Fe1 site in Fe16N that are most favorable for Co, both of which have the longest distance to N atoms. These results suggest that the Co-N interaction is repulsive in FeN lattices, leading to retaining of Fe-N lattice with few Co doping in our experiments. Moreover, the Es dependence on tensile strain (ε) for different Fe-N alloys is plotted in Fig. 6b. We applied biaxial (0 0 1) inplane strain (εxx = εyy) to FeN, whilst left the [0 0 1] direction of the film free to relax. As the ε increases, the Es of Co substituted Fe4N at Fe2 site raises up rapidly, but decreases for Co substituted Fe16N2 at Fe3 site. This brings about a critical strain (εc) as marked with the arrow in Fig. 6b, which corresponds to the case of equal Es for Co substituting Fe4N and Fe16N2. When ε is lower than εc (region I), the Es of Co substituted Fe4N is lower than that of Co substituted Fe16N2, implying the
Fig. 6. Synergistic effect of lattice strain and Co substitution on thermostability tunability by first-principles calculations. (a) Structures of Fe4N, Fe16N2, and Fe16N, displaying inequivalent Fe sites. (b) Dependence of solution heat Es on tensile strain (ε) for different Fe-N alloys. (c) Es variation of Co substituted (Fe1-yCoy)16N2 cell with y.
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appropriate Co doping is very important for improving thermostability and maintaining high magnetism simultaneously.
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4. Conclusion This paper presents the synergistic effect of lattice strain and Co doping on thermal stability of FeN films. Under the tensile strain, an appropriate Co doping succeeds in improving thermostability and maintaining high magnetism of the film simultaneously. Accordingly, we constructed a Fe/Cr/FeN:Co heterostructure with adaptable magnetism (MS ranging 2.4–2.8 T) and high thermostability (bearing 450 °C annealing). The synergistic effect was found to be related to the solution heat tunability of Fe-N system. These findings may promote the FeN film towards the practical applications, such as magnetic writing heads and permanent magnets. Declaration of competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Key Research and Development Program of China (No. 2016YFA0201002), the National Science Foundation of China (Nos. 51671023, 51871017), the Beijing Natural Science Foundation (2192031), the Key Science and Technology Projects of Beijing Education Committee (No. KZ201810011013), and the Program of Beijing Laboratory of Metallic Materials and Processing for Modern Transportation. S.O. acknowledges support from the Elements Strategy Initiative for Structural Materials (ESISM) and the JSPS KAKENHI Grant Nos. JP17H01238 and JP17K18827. References [1] A. Moser, K. Takano, D.T. Margulies, M. Albrecht, Y. Sonobe, Y. Ikeda, S.H. Sun, E.E. Fullerton, Magnetic recording: advancing into the future, J. Phys. D Appl. Phys. 35 (2002) 157–167. [2] M. Barbic, S. Schultz, J. Wong, A. Scherer, Recording processes in perpendicular patterned media using longitudinal magnetic recording heads, IEEE Trans. Magn. 37 (2001) 1657–1660. [3] M. Alex, A. Tselikov, T. McDaniel, N. Deeman, T. Valet, D. Chen, Characteristics of thermally assisted magnetic recording, IEEE Trans. Magn. 37 (2001) 1244–1249. [4] D. Speliotis, Magnetic recording beyond the first 100 Years, J. Magn. Magn. Mater. 193 (1999) 29–35. [5] S. Sugimoto, Current status and recent topics of rare-earth permanent magnets, J. Phys. D Appl. Phys. 44 (2011) 064001. [6] S. Hirosawa, M. Nishino, S. Miyashita, Perspectives for high-performance permanent magnets: applications, coercivity, and new materials, Adv. Nat. Sci-Nanosci. 8 (2017) 013002. [7] K. Atallah, D. Howe, A novel high-performance magnetic gear, IEEE Trans. Magn. 37 (2001) 2844–2846. [8] T. Chin, Permanent magnet films for applications in microelectromechanical
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