Young’s modulus of the ribbon

The magnetostriction is a dependence of Young’s modulus E of a magnetic material on its state of magnetization. When an originally demagnetized specimen is saturated, its modulus increases by an amount ∆E. The value of

∆E/E0

Fig. 5.6 shows the normal σ vs. ∆ε plot, which plot is called normal, because it is concave up, as shown in Refs. 2, 3, and 38. That is, the slope of the dotted fitting line (slope I) is smaller than that of the solid fitting line (slopeII). At the intersection of the slopes I and II lines, we can define the critical internal stress (σ

depends greatly on the way in which it is measured, as will be explained below[2].

ic) of the ribbon[3,38]. The physical meaning of σic can be considered as the critical transition point for the ribbon sample from the demagnetized state to the saturation state through the magneto-elastic mechanism; e.g., Fig. 8.26 of Ref.

14. Moreover, from slope II, we can determine the Young’s modulus (ES) in the saturated state. Also, from slope II and the intercept of the solid fitting line, we can find the elastic strain ∆εel and magneto-elastic strain ∆εme

𝐸₀ = σ

∆𝜀_𝑒𝑙 + ∆𝜀_𝑚𝑒 (5.1)

[14, 22]. As a result of these two kinds of strain, the modulus in the demagnetized state is[2]

and the modulus in the saturated state is

89

𝐸_𝑠 = σ

∆𝜀_𝑒𝑙 (5.2)

These two relations lead to

∆𝐸

𝐸₀ = 𝐸_𝑠 − 𝐸₀

𝐸₀ =∆𝜀_𝑚𝑒

∆𝜀_𝑒𝑙 (5.3)

For sample of the Fe₈₁Ga₁₉ ribbon, we fixed σ = 25 Mpa to calculate ES and

∆E/E0 by Eq. 5.2 and Eq. 5.3. In Fig. 5.7, we find ES of the Fe81-zNizGa19

ribbons is in the range 115 to 52 GPa. In Fig. 5.8, we find ∆E/E0 is in the range 14% to 115%. In Fig. 5.9, σic not change a lot between Fe81Ga19 and Fe₇₈Ni₃Ga₁₉, as z increases from 3 to 19 in Fe_81-zNi_zGa₁₉, σic increases, and σic

decreases at z = 24. There are two points to be noted here. Firstly, the

Fe57Ni24Ga19 has phases other than A2 phase existing in the ribbon, which may account for the deviation of the general trend in this series of ribbon. (As can be seen in Fig. 5.7- 5.9 and Fig. 5.12 in the next section.) Secondly, we were unable to obtain reliable data from Fe68Ni13Ga19 ribbon. The reason is not clear at present, and further investigations are need.

90

Fig. 5.6 The stress (σ) vs. strain (∆ε) curves of the as-spun Fe81Ga₁₉

0 5 10 15 20 25

40 50 60 70 80 90 100 110 120

Fe

_81-z

Ni

_z

Ga

₁₉

z (at. %) E s (Gp a )

ribbon.

Fig. 5.7 The Young’s modulus in the saturated state (Es) plotted as a function of z.

91

92

5.5 Magnetostriction data

The magnetostriction (λ) hysteresis curve of the Fe81Ni₃Ga₁₉ ribbon, under an external weight w = 208.6 g, which means the external stress σ= 25.7 MPa, is shown in Fig. 5.10. By applying a horizontal field HE, up to + 6 kOe, we tried to turn 𝑀��⃑_𝑠 toward the transverse (or + x) directions, by 90^o. Due to the reason of stress anisotropy, we could not support enough external field to saturate λ.

As expected, the λ vs. HE plot in Fig. 5.10 is symmetric, and ∆λ decreases from zero to -95 ppm for the as-spun Fe81Ni3Ga19

In Fig. 5.11, we still summarize all the values under the varied external weight and the same external field (6000 Oe) for the series of the melt-spun Fe

ribbon.

81-zNizGa19 ribbons. According to Ref. 13, they found that for the rapidly quenched Fe78Ni7Ga15 ribbon, its λ < 200 ppm under 6 kOe external field, which is roughly in agreement with our finding. In this study, that is the largest magnetostriction in the Fe74Ni7Ga19

Although we could not provide enough external field to saturate the sample, λ

ribbon.

s could be calculated from the ∆E effect. This effect since the applied stress causes a deformation through the change in domain magnetization in addition to the elastic deformation. In general, the deformation (∆εme) is caused by rotation magnetization or a displacement of 90^o walls, but no deformation can be induced by 180^o wall displacement. The relation of the

∆εme and λs in polycrystalline can be written as[2, 3]

93

∆ε_𝑚𝑒 =3𝜆_𝑠²

5𝐾_𝑢 ∆ε_𝑒𝑙. (5.4)

Since this gives the additional elongation,

3𝜆_𝑠² shows the sample of the ∆λ which is not saturated by external field, while Fig.

5.12 shows the sample of the λ

can be calculated. The results are shown in Fig. 5.12.

s which was calculated from the ∆E effect. In this study, we found that the values of ∣∆λ∣ in Fig. 5.11 are larger than the values of λs in Fig. 5.12. Since the Ni addition in Fe81Ga19 let the ribbons become more isotropic in magnetic anisotropy. When Ku≒0, ∆E effect would diverge. This reason makes the ∆E effect not be ideally used to calculate λs. But the ∆E effect model still shows that reducing Ku is good for the magnetic material.

94

Fig. 5.10 Magnetostriction of the Fe81Ni3Ga19 ribbon plotted as a function of a horizontal in-plane field under an external weight w = 208.6 g.

100 150 200 250 300 350 400 450 -160

Fig. 5.11 Under the 6 kOe external field, plotted the ∆λ VS. w for the series of the melt-spun Fe81-zNizGa19 ribbons.

95

0 5 10 15 20 25

0 20 40 60 80 100

120 Fe _81-z Ni _z Ga ₁₉

z (at. %) λ s (ppm )

Fig. 5.12 The melt-spun Fe_81-zNi_zGa₁₉ saturation magnetostriction (λs) is calculated by ∆E/E0, Es and σic.

96

6 Conclusions

6.1 For Films

We have made series of Fe81-xNixGa19/Si(100) and Fe81-yNiyGa19/glass films, with 0 x or y 26 at.%Ni, at room temperature by the magnetron sputtering method. Magnetic hysteresis loop, magnetostriction, and FMR measurements were performed on these films. Line width mechanisms of ∆H have been studied by many investigators. The most comprehensive channel of the dissipation of the energy from the precessing spin system is that through the eddy-currents induced by the precessing magnetization. Besides the effect of eddy currents, the hopping motion of electrons causes another route of energy dissipation, as first pointed out by Verwey[47]. Yager, Galt, and Merritt find the anisotropy forces the magnetization to rotate parallel to the direction of easy magnetization, and, for the same reason, rotation of magnetization may cause a change in the arrangement of two kinds of ions such as to rotate the easy direction toward the direction of magnetization[2, 48]. Thus the precession motion the magnetization is expected to cause a hopping of electrons, which is accompanied by loss of energy. In this study, we find the addition of Ni into Fe81Ga19 films that causes refined the magnetic anisotropy energy which let the HK decreases, 13.8 – 6.3 Oe, as at% Ni increases. On the other hand, we observed that (∆H)exp of each film is in general asymmetric. Hence, (∆H)exp is composed of two parts: (∆H)exp = (∆H)S + (∆H)A, where (∆H)A and (∆H)A are the symmetric and asymmetric parts. The explanation for this asymmetry is

97

believed to be related to the degrees of the structural and/or magnetic inhomogeneities in each film.

From Ref. 22, λs is 132 ppm for A2, -7 ppm for D0₁₉, and -32 ppm for L1₂, such that the D019 phase and L12 phase are detrimental to saturation magnetostriction. In this study, when y = 22 at.%Ni, there is only one single A2 phase, and when y =0, 4, 11, and 17 at.%Ni, there are mixed phases with A2 (major) and D0₁₉ and/or L1₂ phases (minor), λs

As x or y increases, we found that [I] 4πM

reaches a maximum at x or y = 22 at.%Ni

s just decreases a little, 16.6 – 15.0 KG, [II] HC is small, 34.4 – 13.8 Oe, [III] λs first increases and reaches a maximum at x or y = 22 at.%Ni, [IV] fFMR decreases, 1.6 – 0.8 GHz, [V] µR

increases, 1212 – 3993, and [VI] α decreases, 0.076 – 0.018. Thus, from this study we conclude that the Fe59Ni22Ga19/glass film should be most suitable for the magneto-electric microwave device application.

98

6.2 For Ribbons

We have made a series of Fe81-zNizGa19 ribbons by the rapidly quenching method. From XRD, these ribbons change the lattices constants which depend on number of z. From VSM studies, we found that the magnetic anisotropy Ku

decreases, as at%. Ni added in. As z increases from 0 to 24 in Fe81-zNizGa19, Ms decreases in general from 170 emu/g to 125 emu/g, and Hc inceases from 4.8 Oe to 11.7 Oe. We also discovered that as z increases from 0 to 19, ∆E/E0

In Ref. 4 and 22, there were added B in FeGa allays, one of the purposes is reduced K

increases. The most important, λ increases at z = 7 at.%Ni.

u. This way also reduces a lot the magnetization. The Ni addition in in FeGa allays not reduced too much magnetization, but reduced Ku

Thus, from this study we conclude that the Fe

.

74Ni7Ga19 ribbon should be most suitable for the magneto-electric device application.

99

7. Appendix

7.1 XRD discussion

In this study, we were unable to identity all diffraction peaks. Fig. 7.1 shows the XRD pattern of the Fe81Ga19 alloy film on Si(100) substrate. There are too many phases in the sample; however, it appears that film samples on the glass substrate are better than these deposited on the Si substrate. As result, our discussions were focused on film samples deposited on the glass substrate. Fig.

7.2 shows the XRD pattern of the Fe57Ni24Ga19 ribbon. Peak I is the peak with

Another disbelieving proof is the Curie temperature which was obtained from magnetic thermal gravimetric (MTG) scan up to 900

ribbon maybe consists of two phases, A2 and γ structure. The tree peaks look like the tree γ peaks respective.

Peak II correspondence γ(111), Peak III correspondence γ(200), and Peak II correspondence γ(220). diffraction peaks, and needs further investigation.

100

Fig. 7.1 XRD pattern of the FeGa alloy film on Si(100) substrate.

30 45 60 75 90

0 500 1000 1500 2000 2500

P e a k II I ( 2 θ= 50. 51

o

) Pe a k IV ( 2 θ= 74. 00

o

)

P eak I (2 θ= 29. 19

o

)

In st e n si ty

2 θ

^

deg.

^

P eak I I ( 2 θ= 43. 41

o

) (110) A 2 (200) A 2 (211) A 2

Fe

₅₇

Ni

₂₄

Ga

₁₉

Ribbon

Fig. 7.2 XRD pattern of the Fe57Ni24Ga19 ribbon with the quenching rate (rotating copper wheel speed) was about 15m/s.

101

Fig. 7.3 MTG scans of the Fe57Ni24Ga19 ribbon.

102

7.2 TEM photo for the Fe

₇₀

Ni

₁₁

Ga

₁₉

/Si(100) film

The cross-section transmission electron microscopy photo of the Fe70Ni11Ga19/Si(100) film is shown in Fig. 7.4. In Fig. 7.4(a), we find that the Fe70Ni11Ga19 alloys deposited on Si(100) substrate similar pillars, and the width of a pillar is quite large, about 25 nm. Fig. 7.4(b) shows the Fe70Ni11Ga19 film with some nano-crystals. Fig. 7.4(c) shows the Fourier transform pattern, which means crystal and amorphous in this film.

103

Fig. 7.4 The cross-section transmission electron microscopy photo of the Fe70Ni11Ga19/Si(100) film. (a) The Fe70Ni11Ga19 alloys deposited on Si(100) substrate similar pillars. (b) This shows the polycrystal substrate. (c) Shows the Fourier transform pattern.

104

7.3 σ vs. ∆ε of the Fe

₆₈

Ni

₁₃

Ga

₁₉

ribbon

We could not obtain reasonable E_s, ∆E and σic in the Fig. 7.5. The strain (∆ε) are to small too let the Es

unreasonable larger than 900 MPa.

0 60 120

0 30 60 90

Slop III Slop II

Slop I

Fe ₆₈ Ni ₁₃ Ga ₁₉ Ribbon

σ (MP a )

∆ε (ppm)

Fig. 7.5 The stress (σ) vs. strain (∆ε) curves of the as-spun Fe68Ni₁₃Ga₁₉ ribbon.

105

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109

Biographical Notes

Chi-Ching Liu (劉奇青)

Sex : Male

Date of Birth : September 23, 1982

E-mail:

Education:

ccliu@phys.sinica.edu.tw

Research interests:

Magnetostriction and application; Magnetic domains and domain walls;

Ferromagnetic resonance

Selected Publications:

1. Magnetic properties of Fe-rich Fe-V alloy films ( Journal of Applied Physics 106, (2009 ) 013901)

2. Effects of Substrate Temperature on Magnetostriction of Fe

62

Co

19

Ga

19

3. Ferromagnetic resonance properties of Fe

/Si(100) Films (ICCE-20 Conference)

81-x

Ni

x

Ga

19

/Si(100) and Fe

81-y

Ni

y

Ga

19

4. Magneto-elastic and mechanical properties of Fe81-xNixGa

/glass films (Journal of Alloys and Compounds 562, 111 (2013))

19

/Si(100) and Fe

_81-y

Ni

_y

Ga

₁₉

5. Magnetic domain studies of La

/glass films (MEMSM 2013 Conference)

0.7

Sr

0.3

MnO3 film deposited on SrLaAlO

3

(001) substrate (J. Phys. D: Appl. Phys., 46, (May 2013), 255001)

2001- 2005: B. Sc., Physics, Fu Jen Catholic University

2005- 2008: M. Sc., Institute of Optoelectronic Sciences, National Taiwan Ocean University

2010-2013: Ph. D., Dept. of Electrophysics, National Chiao Tung Univ.

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