Magnetostrictive properties of Co-Fe alloy epitaxial thin films with Co-rich composition

Co-Fe alloys have recently attracted much attention as one of magnetostrictive materials and have been investigated for applications such as sensors, actuators, vibration energy harvesting devices, etc. Large magnetostriction of +150×10^–6 – +250×10^–6 is observed for Co-Fe alloys with Co-rich compositions,^1–4 where bcc lattice is locally deformed by inclusion of fcc nanocrystals.^2–5 In order to clarify the intrinsic magnetostriction property, it is important to understand the magnetostriction coefficients along <100> and <111>, λ₁₀₀ and λ₁₁₁. However for Co-rich compositions, these values have not yet been made clear. In our previous study,⁶ the magnetostrictive properties of Co-Fe alloys with Fe-rich compositions were investigated by employing epitaxial films. The purpose of the present study is to prepare well-defined Co-Fe alloy epitaxial films with Co-rich composition (Co₇₅Fe₂₅), where bcc single phase is expected to be formed, and to investigate the magnetostrictive properties.

Co-Fe films of 100 nm thickness were prepared on MgO(001) and (110) single-crystalline substrates of 20×20×0.3 mm³ at 300 °C by using a radio-frequency (RF) magnetron sputtering apparatus. A Co₇₀Fe₃₀ (at. %) alloy target of 3 inch diameter was used. The details of deposition condition are similar to those of our previous study.⁶ The film thickness and the composition were confirmed by x-ray reflectivity and energy dispersive x-ray spectroscopy (EDS) to be 100±1 nm and Co - 25±2 at. % Fe, respectively.

The structural properties were investigated by reflection high-energy electron diffraction (RHEED) and x-ray diffraction (XRD) with Cu-Kα radiation (wave length: 0.15418 nm). The magnetization curves were measured by vibrating sample magnetometry. The magnetostriction was observed by employing a cantilever method under in-plane rotating magnetic field up to 1.2 kOe. The details of our measurement system are reported in our previous papers.^6,7

Figure 1(a-1) shows the RHEED pattern observed for a Co₇₅Fe₂₅ film formed on MgO(001) substrate. A diffraction pattern from bcc(001) single-crystalline surface is observed. The arrows show formation of reconstructed surface of c(2×2). A Co₇₅Fe₂₅(001) single-crystalline film with bcc structure is epitaxially grown in the orientation relationship of Co₇₅Fe₂₅(001)[110]_bcc||MgO(001)[100]. Figure 1(b-1) shows the RHEED pattern observed for a Co₇₅Fe₂₅ film formed on MgO(110) substrate. The pattern is analyzed to be an overlap of reflections from two bcc(211) variants, as shown by the spots indexed with the subscripts of A and B. An epitaxial Co₇₅Fe₂₅(211) bi-crystalline film with bcc structure is formed in the orientation relationships of Co₇₅Fe₂₅(211) $[011̄]$_bcc||MgO(110)[001] (type A) and Co75Fe25(211) $[01̄1]$ bcc ||MgO(110)[001] (type B). In this configuration, there exists a large mismatch of –17% along MgO$[1̄10]$ at the Co₇₅Fe₂₅(211)/MgO(110) interface. It is reported that periodical misfit dislocations are preferentially introduced at the interfaces, for example, Co₅₀Fe₅₀(211)/MgO(110)⁸ and Cr(211)/MgO(110)⁹ etc. The presence of such periodical dislocations reduces the effective lattice mismatch from –17% to nearly 0%. Similar phenomenon is considered to be occurred in the Co₇₅Fe₂₅/MgO interface.

Figures 1(a-2) and (a-3) respectively show the 2θ/ω-scan out-of-plane and 2θχ/φ-scan in-plane XRD patterns of Co₇₅Fe₂₅(001) single-crystalline film. Out-of-plane Co₇₅Fe₂₅(002) and in-plane Co₇₅Fe₂₅(200) reflections are observed. The out-of-plane and in-plane lattice spacings are calculated from the peak angles to be d₍₀₀₂₎ = 0.1428 nm and d₍₂₀₀₎ = 0.1416 nm, which agree with the values of bulk Co₇₅Fe₂₅ crystal (a = 0.2837 nm¹⁰) within small differences of less than ±0.7%. The values of full width at half maximum of the ω-scan out-of-plane and φ-scan in-plane rocking curves measured by fixing the diffraction angles, 2θ and 2θχ, at the peak angles of Co₇₅Fe₂₅(002) and (200) reflections were Δθ_50(002) = 0.53° and Δθχ_50(200) = 0.58°, respectively (not shown here). Figures 1(b-2) and (b-3) show the XRD patterns of Co₇₅Fe₂₅ bi-crystalline . It is considered that Co₇₅Fe₂₅(211) reflections from the two variants are overlapped in the out-of-plane pattern and that the Co₇₅Fe₂₅$(011̄)$ reflection from A-type variant and the Co₇₅Fe₂₅$(01̄1)$ reflection from B-type variant are overlapped in the in-plane pattern. The out-of-plane and in-plane lattice spacings are calculated to be d_(211)A,B = 0.1159 nm and $d(011̄)A+(01̄1)B$ = 0.2012 nm, where the differences with respect to the bulk values are found to be less than +0.3%. The Δθ_50(211)A,B and the $Δθχ50(011̄)A+(01̄1)B$ were respectively 0.94° and 1.96°. These results show that the bcc-Co₇₅Fe₂₅ films formed on both the MgO(001) and (110) substrates are high quality epitaxial films with small strain.

Figure 2(a-1) shows the magnetization curves measured for the Co₇₅Fe₂₅(001) single-crystalline film. The easy magnetization direction is parallel to [110], which is obtained by projecting [111] on the (001) surface as shown in Fig. 2(a-2). On the other hand, the hard magnetization direction is observed along [100]. Therefore, the in-plane magnetic anisotropy is reflecting the magnetocrystalline anisotropy of Co₇₅Fe₂₅ bulk alloy material¹¹ with the easy <111> and hard <100> axes and the demagnetization field. Figure 2(b-1) shows the magnetization curves measured for the Co₇₅Fe₂₅(211) bi-crystalline film. The easy magnetization direction is not observed along $[11̄1̄]A+[1̄11]B$ but along $[011̄]A+[01̄1]B$⁠. $[11̄1̄]A+[1̄11]B$ is parallel to the direction obtained by projecting [100]_A and [100]_B on the (211) surface as shown in Fig. 2(b-2). The in-plane magnetic anisotropy is influenced not only by the magnetocrystalline anisotropy but also by the demagnetization field, as shown in the case of Co₇₅Fe₂₅(001) single-crystalline film. Therefore, the film is considered not to be easily magnetized along $[11̄1̄]A+[1̄11]B$ due to contributions from both easy (⁠$[11̄1]Aand[1̄11]B$⁠) and hard ([100]_A and [100]_B) axes. On the contrary, the hard magnetization direction is observed along $[2̄1̄5]A+[2̄1̄5]B$⁠, which is expected by projecting [001]_A and [001]_B. These magnetization behaviors also show that Co₇₅Fe₂₅(001) single- and (211) bi-crystalline films with good crystallographic quality are obtained in the present study.

When magnetization coherently rotates in a (001) single-crystalline film under an in-plane rotating magnetic field, the relative length variations along [100] and [110], Δl/l_[100] and Δl/l_[110], are respectively given as⁶ 

where ψ is the angle of magnetic field direction with respect to [100]. Figures 3(a-1) and (a-2) show the Δl/l_[100] and Δl/l_[110] measured for the Co₇₅Fe₂₅(001) single-crystalline film under rotating magnetic field of 1.2 kOe. Figure 3(b) summarizes the magnetic field dependences of the amplitudes of Δl/l_[100] and Δl/l_[110]. The λ₁₀₀ and the λ₁₁₁ values are estimated from the saturated amplitudes to be +60×10^–6 and +150×10^–6, respectively.

The relative length variations measured for a (211) bi-crystalline film along $[011̄]A+[01̄1]B$ and $[11̄1̄]A+[1̄1̄1]B$⁠, $Δl/l[011̄]A+[01̄1]B$ and $Δl/l[11̄1̄]A+[1̄11]B$⁠, are respectively given as⁶ 

where ξ is the angle of magnetic field direction with respect to $[011̄]A+[01̄1]B$⁠. Figures 4(a-1) and (a-2) show the $Δl/l[011̄]A+[01̄1]B$ and $Δl/l[11̄1̄]A+[1̄11]B$ measured for the Co₇₅Fe₂₅(211) bi-crystal film under rotating magnetic field of 1.2 kOe. Figure 4(b) shows the amplitudes of $Δl/l[011̄]A+[01̄1]B$ and $Δl/l[11̄1̄]A+[1̄11]B$ as a function of magnetic field. The λ₁₀₀ and the λ₁₁₁ values are calculated from the saturated values to be +55×10^–6 and +185×10^–6, respectively.

Figure 5 summarizes the compositional dependences of λ₁₀₀ and λ₁₁₁ of (001) single- and (211) bi-crystalline films. Here the values measured for Fe, Co₃₀Fe₇₀, and Co₅₀Fe₅₀ epitaxial films⁶ are shown for comparison. The single- and the bi-crystalline films show similar λ₁₀₀ and λ₁₁₁ values for the respective compositions. λ₁₀₀ value increases with increasing the Co composition up to 50 at. %, and then drastically decreases with further increasing the Co composition. On the contrary, λ₁₁₁ value monotonously increases as the Co composition increases from 0 to 75 at. %. The Co₇₅Fe₂₅ films have positive moderately-large λ₁₀₀ and fairly-large λ₁₁₁ values.

Co₇₅Fe₂₅(001)_bcc single- and (211)_bcc bi-crystalline films are obtained on MgO(001) and (110) substrates, respectively. The lattice spacings of Co₇₅Fe₂₅ films agree with the bulk values within small differences of less than 1%. The orientation dispersions are less than 2°. The magnetic and the magnetostrictive properties are investigated by using the well-defined epitaxial films. The in-plane magnetic anisotropies of single- and bi-crystalline films are reflecting the magnetocrystalline anisotropy and the demagnetization field. The (λ₁₀₀, λ₁₁₁) values of single- and bi-crystalline films are determined to be (+60×10^–6, +150×10^–6) and (+55×10^–6, +185×10^–6), respectively. The magnetostrictive properties revealed by using well-defined epitaxial films are believed to enhance the future studies and applications of Co-Fe alloy materials.

This paper is based on results obtained from a project, 20002152-0, subsidized by the New Energy and Industrial Technology Development Organization. Authors thank Mr. Naoki Yoshihara of Instrumental Analysis Center at Yokohama National University for his excellent technical supports for XRD and EDS measurements.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.