Magnetostriction and volume magnetostriction of sputtered Tb20Fe24Co56 film

The magnetostriction and volume magnetostriction of sputtered amorphous Tb20Fe24Co56 (TFC) films are investigated. In recent years, knowledge of volume magnetostriction is needed in terms of actuator applications utilizing the volume magnetostriction effect. This TFC film with the composition selected in this study is known to exhibit small Joule magnetostriction in Tb-Fe-Co system, and the volume magnetostriction of Tb-Fe-Co thin film systems may be observed more significantly. A bilayer cantilever structure is used to evaluate the magnetostriction performance, which indicates that the largest magnetostriction coefficient and volume magnetostriction of the TFC films are 54 and 48 ppm at an external magnetic field of 7490 Oe, respectively. The Ar gas pressure during sputter deposition is selected to be in the range of 0.7 to 8 Pa in consideration of the deposition quality of the TFC film. The residual stress shifts to the tensile side as the Ar gas pressure increases while the stress field affects the magnetostriction performance. The value of the Joule magnetostriction of the TFC film is almost as same as the volume magnetostriction, which shows that the volume magnetostriction is the dominant mechanism of the magnetic field-induced strain. The homogeneous distribution of elements in the amorphous TFC films possibly makes the Joule magnetostriction small. Since the magnetization of the TFC film is sensitive to strain, the stress field in the in-plane direction strongly constrains the magnetic moment in the out-of-plane direction, and this constraint affects the magnetostriction and magnetization properties. This strain-sensitive magnetic film opens up new possibilities for microdevices using magnetostrictive TFC films via volume magnetostriction.


Introduction
In recent years, magnetostriction properties of rare-earth-transition metal films have attracted much interest in sensitive, low-power spintronic devices and other magnetostriction microdevices [1][2][3][4][5][6][7][8][9][10][11][12].Among giant magnetostrictive materials, FeGa is well known because of its low cost and easy manufacturing process [13][14][15].Although FeGa has a high magnetostriction performance, the effective magnetostriction coefficient (λ eff ) of asdeposited FeGa film is less than 100 ppm [15,16].In contrast, thin films of rare-earth-transition metal alloys, such as TbFe-based alloys, which have enormous magnetostrictive performance, are considered to be promising materials for magnetostrictive devices.All of their alloys, such as TbFeDy (2000 ppm) [17,18] and Tb 31.7 Fe 13.6 Co 54.7 (1500 ppm) [19] have a higher effective magnetostriction coefficient than that of FeGa.While TbFeDy has such a high magnetostriction performance, it demands a high-temperature process for synthesizing TbFeDy compounds [18].Therefore, these devices are difficult to realize with general microfabrication processes and also increase the cost of microdevice development.On the other hand, the TbFeCo films do not require a specific process and can be obtained by using sputtering at room temperature [20][21][22][23][24][25].Compared to other amorphous magnetostritive materials (λ eff < 100 ppm), such as CoFeSiB and TbFe films [26,27], the amorphous TbFeCo films show a larger magnetostriction performance (λ eff > 1000 ppm) [20] and it is also reported that electrodeposited FeCo films with Tb impurity exhibit the large volume magnetostriction [28].The volume magnetostriction, generated by magneto-volume effect [29], is independent of the motion of the magnetic domain.It also attracts interest in microdevices with thin magnetic films with large volume magnetostriction, such as a magnetic field sensor [30].Moreover, a spin-current volume effect in the magnetostrictive material is also reported, where volume magnetostriction has shown high potential for actuator applications [31].
The main objective of this study is to evaluate the volumetric magnetostriction of the sputtered Tb 20 Fe 24 Co 56 (TFC) films, and the composition of Tb with small Joule magnetostriction is selected for investigation.It has been reported that TbFeCo films with 20 at% Tb [19] have smaller Joule magnetostriction than TbFeCo films with higher Tb compositions [20][21][22][23][24][25].The Tb-Fe-Co system shows a eutectic reaction [32], which forms TbFe and TbCo phases in equilibrium.However, near the compositions of Tb 20 Fe 24 Co 56 , a solid solution phase exists, which means that the composition distribution of elements of Tb 20 Fe 24 Co 56 becomes more homogeneous than other compositions in the Tb-Fe-Co system.The amorphous phase is not an equilibrium state, but for such a composition, the driving force of atom diffusion becomes small, resulting in homogenous composition.It can be one reason for the small Joule magnetostriction of the TbFeCo film with a composition near Tb 20 Fe 24 Co 56 [19,32,33].
In this work, we chose the TFC film with this composition and investigated the volume magnetostriction and Joule magnetostriction of the RF-sputtered films for applications of future microdevices based on volume magnetostriction.

Fabrication process of the test specimen of TFC film
In order to investigate the effect of Ar gas pressure P Ar on the internal stress and the magnetostriction property of TFC films, sputter deposition is performed using an RF magnetron sputter (ULVAC ® ) under various Ar gas pressure with a constant RF power of 50 W for 20 min at room temperature.A 20 mm × 20 mm polyimide plate as the substrate is fixed on a Si wafer in the sputtering process.The distance from the Tb 20 Fe 24 Co 56 target (Kojundo Chemical Lab ®) to the sample is 60 mm.Besides, the base pressure is lower than 10 −4 Pa, and the Ar flow rate is maintained at 11.4 sccm.After the deposition of the TFC film, Energy Dispersive x-ray Analysis (EDX) is employed to analyze the elemental composition of the sputtered TFC films with a thickness of 40-200 nm, and the thickness of the films is measured by EDX-thickness monitoring.The SEM image of the film surface and the element distribution (Tb, Fe, Co) by scanning electron microscope (SEM) with EDX mapping analysis is shown in figure 1(a).It indicates that the surface is very smooth and elementary distribution is very uniform.The pressure dependence of the thickness of the TFC film with a deposition time of 20 min is shown in figure 1(b).
For analyzing the amorphous structure of the sputtered TFC film, the atomic force microscope (AFM) is used to profile the morphology of the TFC film on a Si wafer, as shown in figure 1(c).The x-ray diffraction (XRD) is shown in figure 1(d), and the absence of peaks other than the Si substrate peak indicates that the TFC film is an amorphous structure.From those results, it is found that the morphology of the TFC film is uniform without any significant crystalline grains.

Experimental setup and method for evaluating the magnetostriction performance of TFC films
A bi-layer cantilever method is used to measure the magnetostriction performance of the TFC films, as shown in figure 2. When an external magnetic field is applied to the bi-layered cantilever, and the magnetostriction causes deformation.The displacement of the cantilever is observed by an optical microscope with a spatial resolution of 3.6 μm.A polyimide plate with 25 μm thickness is fixed on a silicon dummy wafer by Kapton ® tapes.After the RF sputtering process, the TFC film on a polyimide plate is cut into 1 mm × 10 mm rectangles, and one end is fixed to a rigid top plate of a pole as a bi-layered cantilever.When the bi-layer cantilever (TFC on Polyimide) bends downward under an applied magnetic field, the displacement δ is defined to be a positive value (δ > 0), and vice versa, the displacement is defined to be negative (δ < 0).To obtain the effective Joule magnetostriction, the longitudinal and transverse magnetostriction are evaluated.The effective magnetostriction coefficient λ eff is given from the displacements under a magnetic field [34,35], where ‖ D , ┴ D , E s , E f , t s , t f , ν s , ν f, and l are the displacement of the cantilever when the length direction is parallel to the magnetic field, the displacement of the cantilever when the length direction is orthogonal to the magnetic field, the Young's modulus of the polyimide plate, the Young's modulus of the TFC film, the thickness of the polyimide plate, the thickness of the TFC film, the Poisson ratio of the polyimide plate, the Poisson ratio of the TFC film, and the length of the bi-layered cantilever.
The curvature of each TFC film is evaluated and measured by the optical camera three times.Furthermore, the residual internal stress σ of TFC film deposited on the flat polyimide plate is calculated from Stoney formula, as given by [36]:  where R is the radius of curvature.In this work, it is assumed that the Poisson ratios of the polyimide and TFC films are 0.3 and 0.33, respectively [37].The Young's modulus of the TFC film is assumed to be 65 GPa [38] as well as Young's modulus of the polyimide plate is evaluated to be approximately 1.86 GPa [39].Moreover, to estimate the magnetostriction performance of the TFC films, the longitudinal magnetostriction l ‖ and transverse magnetostriction l ┴ are also considered to calculate the volume magnetostriction by the equation ω = l ‖ + 2 l ┴ [40, 41].l ‖ and l ┴ are defined from the equation (2) by assuming ‖ D and ┴ D are zero, respectively.

Magnetostriction effect of TFC film in cantilever experiment
The magnetostriction performance of the TFC films is investigated by measuring the displacement of the bilayer cantilever structure under external magnetic fields up to 7490 Oe (TM-YS3FA'02, Tamakawa ®).Figures 4(a

Magnetization measurements of the TFC films
In addition, to evaluate the relationship between the magnetic property of the TFC film and the applied tensile strain, the VSM experiment is executed, and the M-H hysteresis loop curve is obtained.An arch-curved glass holder with a curvature (Φ 18 mm) is used as a sample holder to apply a strain to the film (2 mm × 10 mm), as shown in figure 6.Furthermore, for investigating the longitudinal and lateral magnetostriction performances of the TFC film, a strain parallel to or orthogonal to the external magnetic field are applied to the TFC film.The applied strain ε is obtained by the  where ε, a, p, t, are the applied strain, the distance between the polyimide plate surface and neutral line, the radius of the curvature of the arch-curve glass, and the thickness of the polyimide plate, respectively.It is assumed that the polyimide plate is homogeneous, and the thickness of the TFC film (< 200 nm) is much thinner than that of the polyimide plate.Thus, the neutral line of the bi-layered cantilever is regarded to be in the middle of the polyimide plate.From equation (1), the arch-curved glass holder can induce a strain of approximately 0.1% for the 25 μm-thick polyimide plate.VSM measurements are conducted for the as-deposited TFC films at magnetic fields of −10000∼10000 Oe.Those results indicate that the out-of-plane direction is the easy axis of magnetization, possibly due to stress anisotropy.Besides, figure 7(b) also shows the typical positive magnetostriction (Sample C), measured in the inplane direction with no strain, 0.1% strain parallel to the magnetic field, and 0.1% strain orthogonal to the magnetic field.This 0.1% strain causes a stress change of 65 MPa to the TFC film.Generally, a giant magnetostrictive material causes a significant deformation under the applied magnetic field, and vice versa, and an applied strain can also lead to a significant variation in magnetic properties due to the  rotation of the magnetic domains [20,41].However, magnetostriction measurements indicate that volume magnetostriction is dominant in this film.
In general, it is known that there is the following relationship between volume magnetostriction and magnetization [41].
where c, M, H are the volume, bulk modulus, magnetization, magnetic field and volume magnetostriction w = d , V V (V is the volume).The bulk modulus can be given by [37,38]: If the TFC film on the polyimide substrate is subjected to a strain ε elongated in the longitudinal direction, the film is distorted by -v f ε in the thickness direction, and considering that the film is fixed to the underlying plate, the volumetric strain of the film is (1-v f )ε.In other words, if the Poisson's ratio is v f = 0.33, a 0.1% strain in the longitudinal direction of the TFC film will increase the volume by 0.067%.The length, width, and thickness of Sample C are 1.0 × 10 −2 , 2.0 × 10 −3 , and 8.3 × 10 −8 m, respectively.From equation (5), the volume modulus of Sample C is estimated to be 96 GPa.For both cases of in-plane strains parallel and orthogonal to the magnetic field, the volume magnetostriction expected from the magnetization change from equation (4) is 7.9 × 10 −3 (1/ T).However, the observed volume magnetostriction from the cantilever test is 5.6 × 10 −5 (1/T).There is a large discrepancy.One of the reasons for this discrepancy can be explained by the fact that the anisotropy strength of magnetization varies with the stress field present in the in-plane direction.Bending the TFC film also changes the stress field in the film.This stress field due to the deformation is shown to facilitate a change in the anisotropy strength of magnetization, which is strongly constrained in the out-of-plane direction in the unstrained state.Meanwhile, the saturation magnetization of the TFC film under the applied strain occurs when the applied magnetic field is larger than approximately 2000 Oe.It is considered that the magnetic moments are less constrained in the out-of-plane direction by the applied strain, and the magnetic moments are aligned in the inplane direction by the application of the magnetic field.Although quantitative discussion is difficult because the effect of demagnetization due to the different sample geometries is not taken into account, we believe that the VSM results qualitatively reflect the effect of the volume magnetostriction.

Discussion
While the Ar gas pressure was lower than 4 Pa, the internal compressed stress of the TFC film was saturated to approximately −200 ∼ −300 MPa.Moreover, when the Ar gas pressure increases larger than 5 Pa, the compressive stress of the TFC film becomes lower.According to other reports, the fewer Ar gas could cause a more compact sputtered material to make the film have more compressive stress and vice versa [42,43].When the applied Ar gas pressure is decreased, the mean free path of Ar gas and incident atoms is increased.The energetic incident atoms form a compressive dense film [42,43].In this work, the internal stress of the TFC film was saturated to approximately−300 MPa to −250 MPa when the Ar gas pressure was lower than 4 Pa.In addition, the cantilever test in this work indicates that the magnetostriction coefficient of all TFC films has a similar value in the volume magnetostriction.The maximum Joule and volume magnetostrictions were 54 ppm and 48 ppm, respectively.
According to the phase diagram of the Tb-Fe-Co system, Tb 20 Fe 24 Co 56 has few crystalline phases with different compositions in equilibrium due to invariant reactions [32].However, there is a solid solution phase near the composition of the TFC film selected in this experiment.The driving force for atom diffusion is small in this composition, thus the composition is relatively homogenous than other TFC with different compositions [32,33].Although this amorphous sample is in a non-equilibrium state, the situation is the same.It is well known that homogenous amorphous magnetic materials exhibit low Joule magnetostriction.In contrast, the volume magnetostriction is caused by the magneto-volume effect, which doesn't include the motion of magnetic domains.When an external magnetic field is applied, spontaneous magnetization is induced along the direction of the field, and the resulting interaction between lattice spin moments changes its volume [41,44,45].In addition, the strong stress field changes the anisotropy strength of magnetization.When the magnetic field in the in-plane direction increases in the non-strained initial state, the magnetic moments of atoms tend to rotate gradually.This magnetization change is proportional to the magnetic field; therefore, the volume magnetostriction is proportional to the magnetic field.The neighboring Tb-Tb bonds in TbFe 2 crystal is known to show large positive magnetoelastic coupling [46].The volume magnetostriction observed in the amorphous TFC film possibly originated in the dominant Tb-Tb magnetoelastic coupling.In contrast to this sample, 40% Tb of TFC films shows a large Joule magnetostriction [19], which is possibly caused by inhomogeneous crystal structure caused by crystal phase separation.

Conclusion
Magnetostriction properties of the RF-sputtered TFC films were investigated.The sputtered TFC films exhibit a compressive stress of ∼ −121 MPa and are found to be in an amorphous state.The bi-metal cantilever test exhibited that the TFC film had the magnetostriction (λ eff = 54 ppm) and volume magnetostriction (ω = 48 ppm).The fact that the Joule and volume magnetostrictions show almost the same value indicates that the magnetostriction of this film is caused by the volume magnetostriction.In the VSM experiments, changes in the M-H hysteresis loop curves without and with the application of volume strain are observed, suggesting that this is due to changes in the anisotropy strength of the magnetization associated with changes in the stress field in the film.Even if the amorphous Tb 20 Fe 24 Co 56 film is isotropic and homogeneous in element distribution, the stress field in the film has a significant effect on its magnetostriction and magnetic properties.In homogenous amorphous films, the effect of Joule magnetostriction becomes small, and volume magnetostriction becomes dominant.This opens up new possibilities for microdevices using magnetostrictive TFC films via volume magnetostriction.

Figure 1 .
Figure 1.(a) SEM image of the TFC surface and elements distribution (Tb, Fe, Co) observed by EDX mapping.(b) Thickness of the TFC film as a function of Ar gas pressure for a deposition time of 20 min.(c) AFM image of the TFC surface.(d) XRD diffraction of the amorphous TFC film on a Si wafer.

Figure 2 .
Figure 2. Schematic of the bi-layer cantilever test of the TFC film (a) under a magnetic field parallel to the longitudinal direction of the cantilever and (b) under a magnetic field orthogonal to the longitudinal direction of the cantilever.

3. 1 .
Residual internal stress of TFC film on polyimide plate The results of Ar gas pressure dependence on the residual internal stress of the TFC films deposited at the same Ar gas flow rate are shown in figure 3. It indicates that the residual stress of the TFC film ranges from −300 MPa to −250 MPa at pressures below 4 Pa.When the Ar gas pressure is larger than 4 Pa, the compressed stress of TFC film became lower.The lowest residual stress in TFC film in this work is about −121 MPa.
) and (b) show that the TFC films deposited by different Ar gas pressure exhibit a positive magnetostriction performance ranging from 15 ppm to 54 ppm and the volume magnetostriction ranging from 15 ppm to 49 ppm at 7490 Oe of the magnetic field.In addition, the effect of the Ar gas pressure on magnetostriction performance is shown in figures 4(c) and (d).

Figure 4 (
c) exhibits that magnetostriction of the TFC film with Ar gas pressure of 2 Pa and 5 Pa has a peak of approximately 54 ppm and 44 ppm, respectively.Besides, the Joule magnetostriction of the TFC film with Ar gas pressure of 4 Pa has a small magnetostriction coefficient of 15 ppm.Figure4(d) exhibits that both TFC films at Ar gas pressures of 2 Pa and 5 Pa have a peak of volume magnetostriction up to approximately 48 and 41 ppm, respectively.In contrast, the TFC film with Ar gas pressure of 4 Pa has a relatively low volume magnetostriction (ω = 15 ppm).The linear dependence on the magnetostriction performance suggests that the magnetization anisotropy and volume magnetostriction are involved in the magnetostrictive performance.The effects of the residual internal stress on magnetostriction and volume magnetostriction of the TFC film are shown in figures 5(a) and (b).Figures5(a) and (b) suggest that both Joule and volume magnetostriction of the TFC film have a complex relationship with the film stress.

Figure 3 .
Figure 3. Residual internal stress of TFC film on polyimide plate with Ar gas flow rate 11.4 sccm.

Figure 7 (
a) shows the typical M-H curves plotted in a range of −10000∼10000 Oe for the TFC film (Sample C, P Ar = 5 Pa) with the positive magnetostriction.The measurements are performed under magnetic fields in the in-plane and out-of-plane directions with no strain.

Figure 4 .
Figure 4. (a) Magnetic field dependence on magnetostriction.(b) Magnetic field dependence on volume magnetostriction.(c) Ar gas pressure dependence on magnetostriction.(d) Ar gas pressure dependence on volume magnetostriction.

Figure 5 .
Figure 5.Effect of the residual internal stress on magnetostriction (a) and volume magnetostriction (b) of the TFC film at 7490 Oe of the magnetic field.

Figure 6 .
Figure 6.Schematic of the experimental setup of the VSM (Vibrating sample magnetometer) experiment.

Figure 7 .
Figure 7. (a) Measured M-H hysteresis loop curves of the TFC films (Sample C) under the in-plane and out-of-plane magnetic field without strain (strain = 0).(b) in-plane parallel and perpendicular strain to the magnetic field (b).Measured M-H hysteresis loop curves of the TFC films (Sample C) under the in-plane magnetic field parallel or perpendicular to the strain.