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Yura Maeda, Kosuke Imamura, Mitsuru Ohtake, [Shinji Isogami](https://orcid.org/0000-0001-7230-6090), Tetsuroh Kawai, Masaaki Futamoto, Fumiyoshi Kirino, Nobuyuki Inaba

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[Large magnetostriction in γʹ-Fe4N single-crystal thin film](https://mdr.nims.go.jp/datasets/7caf39b5-82e9-45ec-b120-47af87177b34)

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Large Magnetostriction in γʹ-Fe4N Single-Crystal Thin FilmYura Maeda1, Kosuke Imamura1, Mitsuru Ohtake1, Shinji Isogami2, Tetsuroh Kawai1,Masaaki Futamoto1, Fumiyoshi Kirino3, and Nobuyuki Inaba4AFFILIATIONS1Faculty of Engineering, Yokohama National University, Yokohama 240-8501, Japan2Resarch Center for Magnetic and Spintronic Materials, National Institute for Materials Science, Tsukuba 305-0047, Japan3Graduate School of Fine Arts, Tokyo University of the Arts, Tokyo 112-8551, Japan4Graduate School of Science and Engineering, Yamagata University, Yonezawa 992-8510, JapanABSTRACTAn Fe4N(110) single-crystal film of 50 nm thickness with γʹ phase is prepared through hetero-epitaxial growth on an MgO(110) single-crystal substrate at 400 °C by reactive sputtering. The out-of-plane and in-plane lattice constants agree with those of bulk within small differences less than 0.2% and the orientation dispersions are about 1.2°. The degree of N site ordering in Fe4N structure is estimated to be 0.995. The arithmetical mean surface roughness is as small as 0.3 nm. These data show that a high-quality Fe4N single-crystal film is successfully formed. The Fe4N film shows in-plane magnetic anisotropy with the easy magnetization direction parallel to [001] and with the hard direction parallel to [11 (_)1], which is reflecting the positive magnetocrystalline anisotropy, K1. A large negative λ100 value of –40×10–6 and a fairly-large positive λ111 value of +150×10–6 are observed. The present study has shown that γʹ-Fe4N compound is one of the strong candidates for rare-metal-free magnetostrictive materials. Keywords—Fe4N compound, large magnetostriction, single-crystal thin film, γʹ phase1. IntroductionSoft magnetic materials with large magnetostriction have been studied for applications such as sensors, actuators, vibration energy harvesting devices. Rare-metal free materials are desirable from the viewpoints of natural resource and cost, though RFe2 (R = Tb, Sm, etc.) [1], [2], Terfenol-D (TbxDy1–xFe2) [3], and Fe-X (X = Ga, Co) [4]–[6] alloys have been known as magnetostrictive materials. Fe4N compound with γʹ phase is a soft magnetic material with high saturation magnetization (Ms = 1384 emu/cm3 [7]), positive magnetocrystalline anisotropy constant (K1 = +2.3×105 erg/cm3 [8]), high Curie temperature (488 °C [9]), and high spin polarization ratio (simulation: P = –0.6 [10], experiment: |P| = 0.59 at 7.8K [11]). Recently, a theoretical calculation predicts that it also shows a large magnetostriction coefficient along [100], λ100 = –143×10–6 [12]. However, experimental investigation of the magnetostriction has not been carried out yet.In order to understand the magnetostriction property, it is necessary to determine the magnetostriction coefficients not only along [100] but also along [111], that is, λ100 and λ111. For such purpose, epitaxial single-crystal films are useful [13]–[17], since the crystallographic orientations can be controlled by those of single-crystal substrates. Fe4N single-crystal films have been prepared on single-crystal substrates of MgO(001) [18]–[28], SrTiO3(001) [18]–[22], [29], LaAlO3(001) [18]–[20], [29], [30], MgAl2O4(001) [21], (La0.3Sr0.7)(Al0.65Ta0.35)O3(001) [22], Cu(001) [31], TiN(001) [32], SrTiO3(110) [18], [19], and MgO(111) [33]. The purpose of the present study is to prepare a high-quality Fe4N single-crystal film and to experimentally determine the magnetostrictive coefficients. In the present study, an MgO(110) single-crystal substrate is employ to make the easy Fe4N[001] and the hard Fe4N[11 (_)1] directions lying in the in-plane.2. Experimental ProcedureAn Fe4N film was prepared on an MgO(110) single-crystal substrate of 300 μm thickness at 400 °C by using a system consisting of reactive radio-frequency (RF) magnetron sputtering and reflection high-energy electron diffraction (RHEED) observation chambers. The base pressure of sputtering chamber was lower than 4×10–7 Pa. The substrate was heated at 600 °C before film formation to obtain clean surface. An Fe target (purity: 99.9%) of 3 inch diameter was used. The distance between target and substrate was fixed at 150 mm. The pressure of Ar-N2 mixture gas (purity: 99.9999%) was kept constant at 0.67 Pa, where the ratio of N2 partial to total pressure was set at 5%. The RF power was kept constant at 70 W. The deposition time was 2000 s. The sample was cooled down to room temperature after sputtering and then transferred to RHEED observation chamber. The crystal structure and the orientation relationship between film and substrate were determined by RHEED. The sample was exposed to atmosphere after RHEED observation. The resulting film thickness was estimated by X-ray reflectivity to be 52.5 nm. The lattice constant, the orientation dispersion, and the degree of N site ordering were investigated by X-ray diffraction (XRD) with Cu-Kα radiation (wave length: 0.15418 nm). The chemical state was characterized by X-ray photoelectron spectroscopy (XPS). The surface morphology was observed by atomic force microscopy (AFM). The magnetization curves were measured by vibrating sample magnetometry. The magnetostriction was observed by using a cantilever method [15], [16], [34] under rotating magnetic field up to 1.2 kOe. The relative length variation, Δl/l, was calculated from the following formula,      (1)ΔS is the measured bending, L is the distance between laserbeam points (12.5 mm), t is the thickness, E is the Young’s modulus, v is the Poisson’s ratio, and the subscripts of f and s respectively refers to film and substrate. The E and v values of MgO and Fe4N single crystals are calculated to be (E[001], E[11 (_)1], v[001], v[11 (_)1])MgO = (245 GPa, 336 GPa, 0.23, 0.13) and (E[001], E[11 (_)1], v[001], v[11 (_)1])Fe4N = (238 GPa, 115 GPa, 0.29, 0.40) by using the elastic stiffness values of (C11, C12, C44)MgO = (286, 87, 148) [35] and (C11, C12, C44)Fe4N = (316, 132, 41) [36]. The details of calculation method are shown in our previous paper [15].3. Results and DiscussionFig. 1(a) shows the RHEED pattern observed for an Fe-N film prepared on MgO(110) substrate. Here, the incident electron beam is parallel to MgO[001]. A diffraction pattern from an Fe4N(110) single-crystal surface with γʹ phase is recognized, as schematically shown in Fig. 1(b). The large and the small circles respectively correspond to fundamental and superlattice reflections. An Fe4N(110) single-crystal film is epitaxially grown on the substrate. The crystallographic orientation relationship is determined as Fe4N(110)[001] || MgO(110)[001], as shown in Fig. 1(c). In this configuration, there is a fairly large lattice mismatch of about –9.9% at the Fe4N(110)/MgO(110) interface. It is reported that misfit dislocations are periodically formed at interfaces such as Py(001)/MgO(001), Py(110)/MgO(110) [37], Fe-Co(211)/MgO(110) [38], and Fe4N(001)/MgO(001) [22] and such dislocations reduce the effective mismatch to nearly 0%. In the present case of Fe4N(110) film grown on MgO(110) substrate, periodical misfit dislocations are considered to have been also introduced in the film near the interface.Fig. 2(a-1) shows the out-of-plane XRD pattern, whereas Figs. 2(b-1) and (c-1) show the in-plane XRD patterns measured by making the scattering vectors parallel to MgO[11 (_)0] and MgO[001], respectively. Fe4N 110, 11 (_)0, and 001 superlattice reflections are recognized in addition to Fe4N 220, 22 (_)0, and 002 fundamental reflections in the patterns of Figs. 2(a-1)–(c-1), respectively. The XRDs confirm the formation of Fe4N(110) single-crystal film with γʹ phase and the epitaxial orientation relationship determined by RHEED. The lattice constants are calculated to be (a, b, c) = (0.3804 nm, 0.3804 nm, 0.3799 nm) by using the relations of a = b = (2d2202 + 2d22 (_)02)1/2 and c = 2d002. These values are in agreement with the value of bulk γʹ-Fe4N crystal (a = 0.3797 nm [9]) within small differences less than 0.2%. Figs. 2(a-2)–(c-2) show the rocking curves measured by fixing the diffraction angles at the peak angles of Fe4N 220, 22 (_)0, and 002 reflections, respectively. The values of full width at half maximum, Δθ50_Fe4N 220, Δθχ50_Fe4N 22 (_)0, and Δθχ50_Fe4N 002, are about 1.2°. The lattice strain and the film orientation dispersion are very small, though there exists a lattice mismatch of –9.9% at the film/substrate interface. These results also suggest that the mismatch is reduced by introduction of misfit dislocations.Fig. 3 shows the XPS spectrum scanned from 410 to 390 eV, where the binding energy of 1s electron in N atom can be measured. A single peak is observed at 397.2 eV, which does not agree with the energy corresponding to N-N (403.9 eV) [39] but to N-Fe (397.3 eV) [40] bond. Therefore, N-Fe bond is formed in the Fe4N(110) single-crystal film.The ordering of N site in Fe4N lattice is characterized by the intensities of Fe4N(110) superlattice and (220) fundamental XRD reflections. Fe atoms take corner and face-centered positions, (ux, vx, wx) = (0, 0, 0), (0, 1/2, 1/2), (1/2, 0, 1/2), and (1/2, 1/2, 0), while N atom is located at the body-centered position, that is, (uy, vy, wy) = (1/2, 1/2, 1/2). However, there is a possibility that N atom takes one of the three other equivalent octahedral interstitial positions, (uz, vz, wz) = (0, 0, 1/2), (0, 1/2, 0), and (1/2, 0, 0). The order degree (S) is thus defined as the correctness of N atom position. The structure factors (F) of (110) and (220) are expressed asF110 = (rN + rvac – 1)fN        (2)andF220 = 4fFe + (rN – 3 rvac + 3)fN,       (3)where rN and rvac are respectively the probabilities that (uy, vy, wy) and (uz, vz, wz) positions are occupied with and without N atom (1/4 < rN < 1, 3/4 < rvac < 1) and f is the atomic scattering factor. rN and rvac are respectively shown by using S as rN = (3S + 1)/4        (4)andrvac = (S + 3)/4.        (5)By substituting these relations into (2) and (3), F110 and F220 are given as F110 = SfN         (6)andF220 = 4fFe + fN,        (7)respectively. The reflection intensity is proportional to FD and the complex conjugate (F*D*), Lorentz-polarization factor (L), and absorption factor (A). Here, D is the Debye-Waller factor. The intensity ratio of Fe4N 110 to 220 reflection, I110/I220, is thus given as      (8)Thus, S is expressed as     (9)The measured I110/I220 value is 0.0342. The S value of Fe4N(110) single-crystal film is estimated to be nearly 0.995, which indicates that N site is highly occupied by N atom in the Fe4N single-crystal film. Fig. 4 shows the AFM image observed for the Fe4N(110) single-crystal film. Flat surface with the arithmetical mean roughness of 0.3 nm is realized. Fig. 5 shows the magnetization curves. The easy and hard magnetization directions are observed along Fe4N[001] and Fe4N[11 (_)1], respectively. The in-plane magnetic anisotropy is reflecting the magnetocrystalline anisotropy (K1 > 0) of Fe4N crystal with the easy axes along <100> and hard axes along <111>. Furthermore, the saturation magnetization is estimated to be 1410 emu/cm3, which is similar to that of powder Fe4N single- phase material (1384 emu/cm3 at 300 K [7]). These magnetic properties also show that a high-quality Fe4N single-crystal film is obtained in the present study.The Δl/l of cubic materials caused by magnetostriction [41] is expressed as, (10)where (α1, α2, α3) and (β1, β2, β3) are respectively the direction cosines of magnetization and length variation. When the magnetization rotates in Fe4N(110) single-crystal film under in-plane rotating magnetic field, the (α1, α2, α3) are expressed as (). When the Δl/l is measured along [001] and [11 (_)1], the (β1, β2, β3)[001] and (β1, β2, β3)[11 (_)1] are respectively expressed as (0, 0, 1) and (). By substituting these relations into (10), the Δl/l[001] and the Δl/l[11 (_)1] are respectively shown as,     (11).     (12)The λ100 and the λ111 values can be respectively estimated from the phases and the amplitudes of Δl/l[001] and Δl/l[11 (_)1], as shown in Figs. 6(a) and (b). Figs. 6(c-1) and (c-2) show the Δl/l[001] and Δl/l[11 (_)1] measured for the Fe4N(110) single-crystal film under rotating magnetic fields. The phases of Δl/l[001] and Δl/l[11 (_)1] are in agreements with those of Figs. 6(a-2) and (b-1), respectively. Therefore, the λ100 and λ111 values are negative and positive, respectively. Fig. 7 summarizes the amplitudes of Δl/l[001] and Δl/l[11 (_)1] as a function of rotating magnetic field. The λ100 andthe λ111 values are estimated from the saturated amplitudes to be –40×10–6 and +150×10–6, respectively. The Fe4N single-crystal film shows a negative large λ100, as predicted by the theoretical calculation [12]. Moreover, a positive larger λ111 value is obtained. The present study has experimentally clarified the magnetostriction coefficients of Fe4N. Therefore, Fe4N compound is one of strong candidates as magnetostrictive materials.4. ConclusionA high-quality Fe4N(110) single-crystal film with γʹ phase is prepared on an MgO(110) substrate to experimentally determine the magnetostriction coefficients, λ100 and λ111. The lattice constants agree with the values of bulk Fe4N material within small differences less than +0.25% and the out-of-plane and in-plane orientation dispersions are about 1.2°. The Fe4N film shows an in-plane magnetic anisotropy reflecting a positive magnetocrystalline anisotropy constant, K1 > 0. A negative large λ100 value of –40×10–6 and a positive fairly-large λ111 value of +150×10–6 are observed. The present study has shown that γʹ-Fe4N compound is one of the strong candidates for rare-metal free magnetostrictive materials.AcknowledgementAuthors thank Mr. Naoki Yoshihara and Ms. Yuko Kaneda of Instrumental Analysis Center at Yokohama National University for their technical supports for XRD and XPS measurements, respectively.ReferencesA. E. Clark and H. S. 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Inaba, “Magnetostrictive properties of Co-Fe alloy epitaxial thin films with Co-rich composition,” AIP Adv., vol. 12, no. 3, pp. 035144_1–4, Mar. 2022.C. Kittel, Introduction to Solid State Physics, 8th ed., New York: Wiley, 2005, pp. 73–85.M. De Jong, W. Chen, T. Angsten, A. Jain, R. Notestine, A. Gamst, M. Sluiter, C. K. Ande, S. van der Zwaag, J. J. Plata, C. Toher, S. Curtarolo, G. Ceder, K. A. Persson, and N. Asta, “Charting the complete elastic properties of inorganic crystalline compounds,” Sci. Data, vol. 2, pp. 150009_1–13, Mar. 2015.M. Ohtake, T. Tanaka, K. Matsubara, F. Kirino, and M. Futamoto, “Epitaxial Growth of Permalloy Thin Films on MgO Single-Crystal Substrates,” J. Phys. Conf.: Ser., vol. 303, pp. 012015_1–6, Jul. 2011.M. Ohtake, T. Nishiyama, K. Shikada, F. Kirino, and M. Futamoto, “Epitaxial growth of bcc-FexCo100–x thin films on MgO(110) single-crystal substrates,” J. Magn. Magn. Mater., vol. 322, pp. 1947–1951, Jan. 2009.H. Tillborg, A. Nilsson, B. Hernnas, N. Martensson, and R. E. Palmer, “X-ray and UV photoemission studies of mono-, bi- and multilayers of physisorbed molecules: O2 and N2 on graphite,” Surf. Sci., vol. 295, pp. 1–12, Feb. 1993.B. M. Biwer and S. L. Bernasek, “Electron spectroscopic study of the iron surface and its interaction with oxygen and nitrogen,” J. Electron Spectrosc. Relat. Phemon., vol. 40, no. 4, pp. 339–351, 1986.R. Becker and W. Doring, Ferromagnetismus, Berlin: Julius Springer, 1939, p. 345.Fig. 1.  (a) RHEED pattern observed for an Fe-N film prepared on MgO(110) substrate at 400 °C. (b) Schematic diagram of diffraction pattern simulated for an Fe4N(110) single-crystal surface by using lattice parameters of a = b = c = 0.3797 nm [9].  The incident electron beam is parallel to (a) MgO[001] or (b) Fe4N[001]. (c) Crystallographic orientation relationship between MgO(110) substrate and Fe4N(110) film.Fig. 2.  (a-1) Out-of-plane and [(b-1), (c-1)] in-plane XRD patterns measured for an Fe4N(110) single-crystal film prepared on MgO(110) substrate. The scattering vector of in-plane XRD is parallel to (b) MgO[11 (_)0] or (c) MgO[001]. (a-2)–(c-2) Rocking curves measured by fixing the diffraction angles at the peak angles of (a-2) Fe4N 220, (b-2) Fe4N 22 (_)0, and Fe4N 002 reflections. The intensity is shown in (a-1)–(c-1) logarithmic or (a-2)–(c-2) linear scale.Fig. 3.  XPS spectrum showing binding energy of N-1s electron for an Fe4N(110) single-crystal film.Fig. 4.  AFM image observed for an Fe4N(110) single-crystal film.Fig. 5.  Magnetization curves measured for an Fe4N(110) single-crystal film.Fig. 6.  [(a-1), (a-2)] Δl/l[001] and [(b-1), (b-2)] Δl/l[11 (_)1] calculated for (110) single-crystal film with (a-1) λ100 > 0, (a-2) λ100 < 0, (b-1) λ111 > 0, and (b-2) λ111 < 0. (c-1) Δl/l[001] and (c-2) Δl/l[11 (_)1] measured for an Fe4N(110) single-crystal film.Fig. 7.  Magnetic field dependences of amplitude of Δl/l[001] and Δl/l[11 (_)1] measured for an Fe4N(110) single-crystal film.image4.emfDll=32l100a12b12+a22b22+a32b32–13image5.emf+ 3l111a1a2b1b2+a2a3b2b3+a3a1b3b1image6.emfsinψ/√2, –sinψ/√2, cosψimage7.emf1/√3, –1/√3, 1/√3image8.emfλ100cos2ψ +3414λ100=Δll[001]image9.emfλ111sin(2ψ3414λ111=Δll[111]arcsin ) +13image10.emf(c)(a)[110]_[001][110]Mismatch:–9.9%2d2204d220_b ac = 2d002FeNMgO(b)440220 130 040 400 310420 240image11.emf10Diffraction angle, 2θ or 2θχ (deg.)30 50 70 90 110Fe4N 110_MgO 220_Intensity, I(arb. unit)(c-1)(b-1)(a-1)–5 5 0Δθ50= 1.24ºω or φ (deg.)(c-2)(a-2)Δθχ50= 1.15º(b-2)Δθχ50= 1.17ºFe4N 001Fe4N 002MgO 002 MgO 004Fe4N 004_Fe4N 220Fe4N 220MgO220Fe4N110image12.emfBinding energy (eV)Intensity(arb. unit)390 410 400N-Fe bond [39] N  N bond [38]4/7image13.wmf200 nm3nm0image14.emfimage15.emf– λ111– λ100Relative length variation, Δl/l[001](a-1)(a-2)2λ100> 0λ100< 01– λ1001λ1004λ100Relative length variation, Δl/l[111]_[001]λ1001– λ100421(b-1)λ111> 01– λ11114λ111λ1112λ111< 0λ11114λ11112(b-2)[110] [001] [110]___[111][112][111][112]___[111][112][111][112]___[110] [001] [110]__[001]_______Rotation angle, ψ (deg.)100  10–6Relative length variation, Δl/l[111]_360 0 90 180 270Magneticfield0.2 kOe0.4 kOe0.6 kOe0.8 kOe1.0 kOe1.2 kOe100  10–6Relative length variation, Δl/l[001]360 0 90 180 270Magneticfield0.2 kOe0.4 kOe0.6 kOe0.8 kOe1.0 kOe1.2 kOe(c-1) (c-2)image16.emfMagnetic field (kOe)0 1.2–5001001500.4 0.8(  10–6)Amplitude of Δl/l[001]orΔl/l[111]_Δl/l[001]50Δl/l[111]_image1.emf= ΔllΔS ts2Es(1 + vf)3 L2tfEf(1 – vs)  .image2.emf[(–SfND110)2√LA110]={[(4fFe+fN)D220]√LA220} .I110I220image3.emfI110S =√ I220[fND110√LA110]         .{[(4fFe+fN)D220]√LA220}