Skin effect

Chapter 2 Brief review of magnetism and relevant effects

2.6 Skin effect

In high-frequency applications, the current in a good conductor tends to shift to the surface of the conductor, resulting in an uneven current distribution in the inner conductor and thereby changing the value of the internal inductances. In the extreme case, the current may essentially concentrate in the “skin” of the inner conductor as a surface current, and the internal self-inductance is reduced to zero.

Then a high-frequency electromagnetic wave is attenuated very rapidly as it propagates in a good conductor. The distance δ through which the amplitude of traveling plane wave decreases by factor of e^-1 (= 0.368) is called the skin depth of a conductor

[17]

δ = (_𝜋𝜇𝑓^𝜌 )^1/2 (2.15)

Where

ρ

is resistivity, f is microwave frequency,

µ

is permeability.

At microwave frequencies, the skin depth of penetration of a good conductor is so small that fields and currents can be confined in a very thin layer of the conductor surface. For example, at 10 GHz it is a very small distance 0.66 µm for copper

[17]

3. Experiments

3.1 Process

3.1.1 Samples for film

This is the flow chart of the experimental process. We checked the film thickness by Dektak3. The film’s structure was shown in the X-ray diffraction data. The Young’s modulus of each film was obtained from the nano-indentation system. The magnetization hysteresis was measured by VSM system. Our main experiments are the magnetostriction hysteresis and FMR measurements.

Sample Preparations

Dektak3

XRD Nano-Indentation VSM

Magnetostriction FMR

3.1.2 Samples for ribbon

This is the flow chart of the experimental process. We checked the ribbon thickness by vernier. The ribbon’s structure was shown in the X-ray diffraction data. The resistivity of each film was obtained from the van der Pauw method.

The magnetization hysteresis was measured by VSM system. Our main experiments are the magnetostriction hysteresis measurements.

Sample Preparations

Thickness

XRD VSM Resistivity

Magnetostriction

3.2 DC magnetron sputtering method

DC magnetron sputtering is a physical rather than a chemical or thermal process in making films in making films. Permanent magnets are used in the sputtering gun in order to shorten the ionization mfp for the displaced atoms that fly randomly inside the vacuum chamber. Then atoms are physically ejected from a target material by high-energy gas ions, usually argon ions[19, 20]. The arrangement is shown in Fig. 3.1. It is necessary to create plasma of ionized gas in the deposition chamber. The presence of stable plasma, created by the gas atoms, is a necessary[3].

The advantages of dc magnetron sputtering are[21]:

1. Multicomponent films can be deposited.

2. Refractor materials can be deposited.

3. Insulating films can be deposited.

4. Good film adhesion is assured.

5. Low-temperature epitaxy is possible.

6. Thickness uniformity over lager planar areas can be obtained.

The disadvantages are:

The source material must be available in sheet form.

Fig. 3.1 Thin film prepared by dc magnetron sputtering.

3.2.1 Process conditions

A series of magnetic thin films, Fe81-xNixGa19/Si(100) and Fe81-yNiyGa19/glass films, with x, y = 0, 4, 7, 11, 17, 22,and 26 at. % Ni, were deposited films by alloy targets and the dc magnetron sputtering method. The dc magnetron sputtering system is shown in Fig. 3.2, and the working conditions are listed as following:

1. The working gas (99.999% argon) pressure was 5 mTorr.

2. The sputtering power were 80W

3. The deposition temperature (TS) was at room temperature (RT).

4. The film thickness was 1000 Å.

Fig. 3.2 shows schematics of the Sputtering system.

3.3 Rapid quenching melt-spun method

A series of magnetic metallic ribbons, Fe81-zNizGa19 with z = 0, 3, 7, 13, and 24, were made by the rapid quenching melt-spun method in a low vacuum chamber, the arrangement is shown in Fig. 3.3[3, 22]. The surface velocity of the rotating copper wheel was about 15m/s. The average thickness (t) of the ribbon is about 0.03 mm and the width (w) is about 4mm, which is shown in Fig.

3.4.

Fig. 3.3 Ribbons preparation by rapid quenching melt-spun.

Fig. 3.4 The samples of ribbon are made by the rapid quenching melt-spun method.

3.4 The Dektak

system

The Dektak³ system is a high precision measuring system which accurately measures surface texture, shown in the Fig. 3.5. Table 3.1 is the technical specifications for Dektak³ system.

3.4.1 Principle of operation

There is the mobile diamond-tipped stylus on Dektak³ to measure the surface texture of the sample. The high precision stage moves a sample beneath the stylus according to a programmed scan length and speed. The stylus on the stage is mechanically coupled to the core of a linear variable differential transformer (LVDT). As the stage moves the stylus on the sample, the stylus rides over the sample surface. The stylus is translated vertically on the surface variations. The information with electrical signals depending on the stylus movement is produced as the core position of the LVDT changes respectively.

An analog signal proportional to the position change is produced by the LVDT, which in turn is conditioned and converted to a digital format through a high precision, integrating analog to digital converter. The results of the digitized signals from a single scan are stored in computer memory for display, manipulation, and measurement, the process figure is shown in Fig. 3.6[23].

Fig. 3.5 shows Dektak³ system

[23]

Table 3.1 Technical specifications

[23]

Vertical data resolution 5 Å maximum Vertical range 65.5 μm maximum Scan length range 50 μm to 30 mm

Stylus tip radius 12.5 μm standard

Fig. 3.6 Block diagram of Dektak³ architecture[23].

3.5 X-ray diffraction (XRD)

Fig. 3.7 shows the incoming beam let each scatterer to re-radiate a small portion of its intensity as a wave. Then scatterers are arranged symmetrically with distance d, these waves will be in sync (add constructively) only in directions where their path-length difference 2dsinθ=nλ, called Bragg's law[26].

In this study, the structural properties were characterized by the X-ray diffraction (XRD) using CuKα1 line (λ = 1.5405 Å). There are shown typical x-ray diffraction patterns in Fig. 3.8 and Fig. 3.9, and other results are shown in chapter 7 appendix.

Fig. 3.7 The schematic illustration of Bragg's law.

Fig. 3.8 The X-ray diffraction figure on series of Fe81-yNiyGa19/glass films.

Fig. 3.9 The X-ray diffraction figure on series of Fe81-zNizGa19 ribbons.

3.6 Nano-indentation system measure

The Young′s modulus (E f) of the each film was obtained from the nano-indentation system, which is shown in Fig. 3.10. From each indentation cycle, the depth of circle of contact (hp) is obtained. For details of the hp

measurement, please refer to Ref. [24]. From a series of indenting tests (i.e., from heavy to light loadings) we can plot the measured E as a function of hp. Usually, Ef is taken in the hp range, where hp = tf /15 to tf

E = E_s + (E_f− E_s)e⁻^h^t^p^∗ , (3.1)

/10. Alternatively, the following empirical equation is used for fitting [25, 27]:

where ES is the Young′s modulus of the substrate, and t* is a fitting parameter.

The solid curves in Fig. 3.11 show the best-fit results, by using Eq. 3.1, for all the Fe81-yNiyGa19/glass films. When hp > 0.05 µm in Fig. 3.11, E tends to approach a fixed value, i.e., ES ≅ 76 GPa [8], of the 0211 Corning glass substrate. The E vs. hp fitting plots for the Fe81-xNixGa19/Si(100) films look similar to Fig. 3.11, except that all the plots are shifted upward, with ES ≅ 130 GPa for the Si(100) substrate[27].

Fig. 3.10

Nano-indentation system.

Fig. 3.11 Solid curves represent the best-fit results of E vs. h_P, where E is the Young′s modulus and hp is the depth of circle of contact, obtained from the nano-indentation measurements, for the Fe-Ni-Ga/glass films[27].

3.7 Electrical resistivity measurement

In this study, we measured the electrical resistivity (ρ) by the collinear

four-probe array, which is shown in Fig. 3.12. ρ is calculated by the equation as,

ρ =

12 × (𝑉⁺− 𝑉₋)

𝐼 ×𝑡𝑊

𝐿 × C (3.2)

where V+ means V2-V1 for +I, V- means V2-V1 for -I, ρ is in unit of µΩ-cm, and C is a correction factor, dependent on both the ratios W/L and /W[28]. Table 3.2 shows the calculated dependence of the correction factor C on W/L and /W.

In our case, C≒1.

Fig. 3.12 The resistivity measured by the collinear four-probe array.

Table 3.2 Correction factor C for the calculation of the resistivity measured with collinear four-point probes placed on a symmetry axis[28].

W/L Circle Square Rectangle Rectangle Rectangle C for dia. d C for /W=1 C for /W=2 C for /W=3 C for /W=4

1.0 0.9988 0.9994

1.5 1.4788 1.4893 1.4893

2.0 1.9454 1.9475 1.9475

3.0 2.2662 2.4575 2.7000 2.7005 2.7005

4.0 2.98289 3.1137 3.2246 3.2248 3.2248

5.0 3.3625 3.5098 3.5749 3.5750 3.5750

10.0 4.1716 4.2209 4.2357 4.2357 4.2357

20.0 4.4364 4.4516 4.4553 4.4553 4.4553

∞ 4.5324 4.5324 4.5324 4.5324 4.5324

3.8 Ferromagnetic resonance (FMR) experiments

The cavity used was a Bruker ER41025ST X-band resonator which was tuned at fR = 9.6 GHz. The films were oriented such that EA//H��⃑_𝑧 and EA⊥h�⃑_rf. The EA means easy-axis. Where H��⃑_𝑧 was an in-plane external field, which varied from 0 to 2 kOe, and h�⃑_rf was the microwave field, ω is angle velocity for z-axis, and z-axis is EA of the film. Configuration is depicted schematically in Fig. 3.13. A typical FMR absorption spectrum of the Fe59Ni22Ga19/glass film is shown in Fig. 3.14, where we can spot an FMR event manifested by an absorption peak at H = H_R and define the half-peak width (∆H)exp. In this case, HR = 671.4 Oe and (∆H)exp = 133.9 Oe were obtained[29].

Fig. 3.13

Ferromagnetic resonance model.

0 500 1000 1500 2000 0.02

0.04 0.06 0.08 0.10 0.12

Fe ₅₉ Ni ₂₂ Ga ₁₉ /glass 100nm

H

=671.4 Oe

H (Oe)

EA//H

( ^∆H ) _exp =133.90 Oe

Ins tens ity

Fig. 3.14 A typical FMR absorption spectrum of the Fe59Ni22Ga19/Glass film at the microwave frequency f = 9.6 GHz.

3.9 Vibrating-Sample Magnetometer (VSM)

Fig. 3.15 shows the vibrating sample magnetometer used for measuring the magnetization as a function of applied field. It is based on the flux change in a coil when a magnetized sample is vibrating nearby. The sample, commonly a small disk, is attached to the end of a nonmagnetic rod, the other end of which is fixed to a loudspeaker cone or to some other kind of mechanical vibrator. The oscillating magnetic field of the moving sample induces an alternating emf in detection coils, whose magnitude is proportional to the magnetic moment of the sample. The alternating emf is amplified, usually with a lock-in amplifier which is sensitive only to signals at the vibration frequency. The lock-in amplifier must be provided with a reference signal at the frequency of vibration, which can come from an optical, magnetic, or capacitive sensor coupled to the driving system. The detection-coil arrangement usually involves balanced pairs of coils to cancel signals due to variations in the applied field. The apparatus is calibrated with a specimen of known magnetic moment, which must be of the same size and shape as that of the sample to be measured, and should also be of similar permeability[3].

The driving system may be mechanical, through a cam or crank and a small synchronous motor, or in a recent commercial instrument, with a linear motor.

In our case, shown in Fig. 3.16, the vibration frequency is generally below 85 Hz, and the vibration amplitude is a few millimeters. The amplitude is fixed by the geometry of the mechanical system or by the drive signal delivered to the linear motor. The amplitude may vary, depending on the mass of the sample and/or the frequency of vibration. One method is to and a second set of

sensing coils. Then the signal from these coils can be used in the feedback loop to maintain constant amplitude of vibration. Alternatively, a portion of the signal from the permanent magnet can be balanced against the signal from the unknown sample, making the method a null method[30].

Extreme care is necessary to minimize vibration of the sensing coils in the field, and to prevent the measuring field from influencing other parts of the system. Note that the VSM measures the magnetic moment m of the sample, and therefore the magnetization M can be obtained.

Fig. 3.15 Vibrating sample magnetometer (VSM) model.

Fig. 3.16 Vibrating-Sample Magnetometer (VSM). Courtesy Lake Shore Cryotronics, Inc.

3.9.1 Measuring hysteresis loops

The field-in-plane magnetic hysteresis loops were obtained by varying sample orientation with respect to the applied field in the vibrating sample magnetometer (VSM) measurements to indentity the easy-axis (EA) and hard-axis(HA)[29]. When the squareness ratio (SQR

≡

M

/M

) is the largest, the corresponding orientation is defined the EA. Similarly, the orientation with the smallest SQR is identified as the HA. A typical example is shown in Fig.

3.17. In most cases, the angular dependence of SQR is roughly sinusoidal with

a period of 180°. For the more, the HA hysteresis loop of the

Fe

Ni

Ga

/glass film in Fig. 3.18(a) shows that (SQR)

= 0.72, H

= 20 Oe, and the anisotropy field (H

K ≡

(1/2)(H

+ H

) ≈ 6.3 Oe). For the same film, its EA hysteresis loop in Fig. 3.18(b) shows that the saturation magnetization (4 πM

≈ 15.8 KG), (SQR)

= 0.99, and coercivity (H

≈ 13.8 Oe). Here, it is interesting to note that since H

≦ H

for all the films, they may be classified as the “inverted” films[31]. A brief summary is listed below:

as x or y increases from 0 to 26, 4 πM

remains almost constant, 16.8–15.8 KG, and H

decreases, 34.4–13.8 Oe, and the reasons would be discussed in next

chapter

.

Fig. 3.17 The in-plane rotation SQR data of the Fe₈₁Ga₁₉/Si film.

0 50 100 150 200

Fig. 3.18 (a) The hard-axis (HA) and (b) the easy-axis (EA) magnetic hysteresis loop of the Fe55Ni26Ga19ﬁlm deposited on a glass substrate. HK is the anisotropy ﬁeld, 4πMS is the saturation magnetization, H_C is the coercivity, and (SQR)HA and (SQR)EA are the squareness ratio along HA and EA, respectively.

3.10 Magnetostrictions

3.10.1 Optical-cantilever magnetostriction experiment for films

The longitudinal and transverse magnetostrictions (λ^∥ and λ^⊥) were measured in an optical-cantilever system[32], as depicted schematically in Fig. 3.19 and Fig. 3.20. The light source was a helium-neon laser. The laser beam was reflected from the sample tip and re-directed on to the position sensitive detector (PSD). Such that the magnetostriction induced are measured[29]. We used the x-direction and y-direction Helmholtz coils to generate the external fields.

The obtained data are substituted into the following expression Ref. [33] to calculate the magnetostriction λs

where L is the sample (or cantilever) length, νS is the Poisson ratio of the substrate, and νf is the Poisson ratio of the films, ∆∥S or ∆^⊥S is the deflection, ∆

∥ or ∆^⊥, of the free end of the cantilever, when the in-plane longitudinal (H∥) or transverse field (H⊥) is above HS. Here, νS is 0.23 for glass, 0.40 for Si(100), νf = 0.22 for all the metallic Fe-Ni-Ga films, and tS of double-side polished Si(100) or glass is particularly thin, about 110 µm. Typical magnetostriction hysteresis loops of the Fe59Ni22Ga19/Glass film (with tf = 110 nm) are shown in Fig. 3.21, giving λS ≈ 27 ppm and HS≈ 15 Oe in the case, respectively.

Fig. 3.19 Optical-cantilever magnetostriction experiment system.

Fig. 3.20 The x-direction and y- direction Helmholtz coils.

3、Y-COIL 4、holder

1、 horizontal plate 2、X- COIL

5、foothold

Fig.

3.21 Typical hysteresis loops for longitudinal and transverse magnetostrictions (λ^∥ and λ^⊥) of the Fe59Ni22Ga19/glass film plotted as a function of the external

field H.

3.10.2 Magnetostriction experiment for a ferromagnetic ribbon sample

In this study, we measured the saturation magnetostriction of a thin ribbon by the strain gauge method was used for our λ measurements[22, 34-36]. The gauge is cemented directly onto the surface of the ribbon sample under test, so that a small change in length are detected the change in the resistance (R) of the gauge. Bearing these considerations in mind, we used the experimental set-up shown in Fig. 3.22, which is similar to that used in Ref. 37. The ribbon sample was clamped by both ends on a brass sample holder; the xy-plane was parallel to

the ribbon. A horizontal in-plane field HE was applied along the + x directions from an electromagnet. The lower-end clamp could slide freely downward or along the y direction by hooking various standard weights over the aluminum ring. Thus, while the ribbon sample was stretched by the weight, it was also guided by two vertical brass rods alongside the ribbon. In this way, we could minimize the twisting and/or bending effects, which can cause spurious signals during the λS

K = 1 + ν + 𝐿𝑑𝜌

𝑑𝐿 (3.4)

measurements. The gauge sensitivity is defined as the relative change in resistance per relative change in length, or the gauge factor, K=

(∆R/R)/(∆L/L). The gauge factor is given by

where L is the total length of the metal or semi-conductor wire the gauge, ∆R is the resistance change, due to the length ∆L, ν is Poisson’s ratio for the wire material, ρ is the resistivity. The strain gauge used was a CEA-13-125UN-120 type with K=2.0-2.2, purchased from Vishay Intertechnology, Inc. When HE=0, we could measure the external stress strain (σ-∆ε) curve plot for each ribbon sample. From the obtained σ-∆ε curves, it is easy to obtain the ES and

∆E/E0, where ∆E = ES - E0, ES is the Young’s modulus of the sample in the magnetically saturated state, and E0 is that in the demagnetized state[3, 38].

Fig. 3.22 A photo of the experimental set-up for the stress-strain (σ-∆ε) and magnetostriction (λ) measurements.

4. Results and discussion for films

4.1 XRD data

Table 4.1 lists the x-ray structure data of the (FeNi)81Ga19 films deposited on glass substrates. Briefly speaking, 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). It is evident that all the FeNiGa films are highly (110) textured.

Table 4.1 Structural properties, the x-ray diffraction peaks, of the

Fe81-yNiyGa19/glass films. I/Imax is the peak intensity ratio. a is the lattice constant.

4.2 FMR data

Fig. 4.1 shows the main resonance field (HR) at fR = 9.6 GHz as a function of the Ni concentration (x or y) for the two series of (FeNi)81Ga19 films, respectively. From this figure, we find that HR increases as x or y increases.

In general, addition Ni replace Fe at.% in alloys to be caused reduced magnetic in rich-Fe alloys. Then needs higher resonance field at the same fR

When at the Kittel mode resonance, the relationship among H

as x or y

where g = fR/(1.40*x) = ν/1.40 represents the g-factor of the material, and ν = γ/2π is the gyromagnetic ratio. Hence, based on Eq. 4.1, the natural (or FMR-K) resonance (at H=0) would occur at fFMR = ν[HK(HK+4πMS)]^1/2 ≒ ν[HK4πMS]^1/2 with HK << 4πMS. The addition of Ni into Fe81Ga19 alloys causes reduced the magnetic anisotropy energy which let the HK decreases, leads to decreases in HK is evident from Fig. 4.2(a). The plot of fFMR vs. x or y is shown in Fig. 4.2(b), which exhibits similar trend of HK(x,y) shown in Fig.

4.2(a). Because 4πMS of the FeNiGa films is almost independent of x or y, it implies that the fFMR of the FeNiGa films depend solely on HK as suggested by the equation fFMR ≒ ν[HK4πMS]^1/2. The fact that both have the same trend with the variations of Ni concentration is consistent with this conjecture. As

other discussed in next paragraph, fFMR should serve as the cut-off (or limiting) frequency (fC

In general, the complex permeability, µ = µ

) for these series of ferromagnetic films.

R – iµI, has an anomalous behavior, with the real part, µR, drops off and the imaginary part, µI, exhibits an absorption peak at a certain high frequency, e.g. fC. For a non-metallic ferromagnet, fC is mainly determined by FMR. For a metallic ferromagnet, according to Fig. 4.17 of Ref. [1], fC should depend on the dimensions, e.g., tf, of the sample. For example, if tf < δ, where δ is the skin depth, fC, the µR or µI

anomaly at f_C is related the FMR effect in the µ vs. f spectrum. On the other hand, if tf > δ, fC, will be dominated by the eddy-current effect[1]. In our case, t_f=100 nm < δ ≈ 650 nm (at f ~ 1 GHz), thus we expect fC = f_FMR

At low frequencies, the definition of rotation permeability for an un-plane uniaxial film, such as the FeNiGa film studied has, is µ ~ µ

for all the FeNiGa films. However, since the FeNiGa films are in each metallic, the eddy-current effect might also play a role and should be considered in the resonance cases. We will come back to this point later.

R = 4πMS/HK. Fig.

4.3(a) shows the calculated µR of the FeNiGa films for variance Ni concentrations. It is evident that in both series of FeNiGa film µR increases with increasing Ni concentrations. This general tendency can be understood as follows. The Snoek’s law derived from the Landau-Lifshitz equation, gives[2, 3],

(μ_R − 1)f_FMR² = (ν4πM_s)². (4.2)

In Eq. 4.2, 4πMS of the FeNiGa films is almost independent of x or y; i.e. it only decreases by 5%, as x or y increases from 0 to 26 at.%Ni. However, based on

Fig. 4.2, (fFMR)² decreases by 64%, as x or y increases similarly. From Eq. 4.2, there should be a trade-off between µR and fFMR for the two series of FeNiGa films. Indeed, as can be seen from Fig 4.3(b), the value of µR×(fFMR)²

For a ferromagnetic film, high speed magnetization switching means low Gilbert damping parameter (α). From Landau-Lifshitz-Gilbert (LLG) equation, the magnetic damping parameter (α) can be written as[40],

remains nearly constant over the range of Ni concentration for FeNiGa films investigated in this study.

α = _ν4πM^Δf^1/2

S , (4.3)

where ∆f1/2 is the full width at half maximum for the absorption peak of µI at resonance. The form is used in a shorted microstrip transmission line perturbation experiment. Alternatively, Eq. 4.3 can also be written as[16],

α = ν(ΔH)_S/2f_FMR , (4.4)

where (∆H)S is the theoretical full width at half maximum of the absorption peak around the main resonance field (HR). Notice that the subscript “s” of

∆H in Eq. 4.4 means that this theoretical ∆H should be, in principle, symmetric with respect to the central peak, HR. In the following, we shall give a reason for this argument. The LLG equation with Kittel mode can obtain the equation[2, 3, 41],

where the angle φ is the rotating field vector h�⃑_rf made a finite azimuthal angle with the magnetization vector M��⃑_S, λ ≡ (ανMS)/(4πµ^o), and H��⃑^0T is an in-plane field with EA//H��⃑. From Eq. 4.5, tan(φ) reaches the maximum value, when H=HR or φ = 90^o

That we can write down the real and imaginary parts of the susceptibility as .

Fig 4.4 shows the result inrepresentation. The width of the absorption curve at half the maximum value or a half-value width can be calculated by putting φ=

45^o, which makes the value of χ" in half of its maximum value.

In other words, if Eqs. 4.5 and 4.6 are combined, we obtain,

μ_I ∝ sin²ϕ ∝ ^H²

H²+(_α¹)²(H−HR)² (4.8)

In Eq. (4.8), µI is a Lorentzian function of H, which means that µI must be symmetric with respect to HR, and by definition the symmetric width (∆H)S ≡ 2αHR, i.e. Eq. 4.4. However, in reality, as shown in Fig. 3.13, the experimental

在文檔中鐵─鎳─鎵合金材料的鐵磁共振與磁彈性質研究 (頁 53-0)

Chapter 2 Brief review of magnetism and relevant effects

2.6 Skin effect

[17]

ρ

µ

[17]

3. Experiments

3.1 Process

Sample Preparations

Dektak3

XRD Nano-Indentation VSM

Magnetostriction FMR

Sample Preparations

Thickness

XRD VSM Resistivity

Magnetostriction

3.2 DC magnetron sputtering method

3.3 Rapid quenching melt-spun method

3.4 The Dektak

system

[23]

[23]

3.5 X-ray diffraction (XRD)

3.6 Nano-indentation system measure

Nano-indentation system.

3.7 Electrical resistivity measurement

W/L Circle Square Rectangle Rectangle Rectangle C for dia. d C for /W=1 C for /W=2 C for /W=3 C for /W=4

1.0 0.9988 0.9994

1.5 1.4788 1.4893 1.4893

2.0 1.9454 1.9475 1.9475

3.0 2.2662 2.4575 2.7000 2.7005 2.7005

4.0 2.98289 3.1137 3.2246 3.2248 3.2248

5.0 3.3625 3.5098 3.5749 3.5750 3.5750

10.0 4.1716 4.2209 4.2357 4.2357 4.2357

20.0 4.4364 4.4516 4.4553 4.4553 4.4553

∞ 4.5324 4.5324 4.5324 4.5324 4.5324

3.8 Ferromagnetic resonance (FMR) experiments

Ferromagnetic resonance model.

0 500 1000 1500 2000 0.02

0.04 0.06 0.08 0.10 0.12

Fe 59 Ni 22 Ga 19 /glass 100nm

H

=671.4 Oe

H (Oe)

EA//H

( ∆H ) exp =133.90 Oe

Ins tens ity

3.9 Vibrating-Sample Magnetometer (VSM)

The field-in-plane magnetic hysteresis loops were obtained by varying sample orientation with respect to the applied field in the vibrating sample magnetometer (VSM) measurements to indentity the easy-axis (EA) and hard-axis(HA)[29]. When the squareness ratio (SQR

M

/M

) is the largest, the corresponding orientation is defined the EA. Similarly, the orientation with the smallest SQR is identified as the HA. A typical example is shown in Fig.

3.17. In most cases, the angular dependence of SQR is roughly sinusoidal with

a period of 180°. For the more, the HA hysteresis loop of the

Fe

Ni

Ga

/glass film in Fig. 3.18(a) shows that (SQR)

= 0.72, H

= 20 Oe, and the anisotropy field (H

(1/2)(H

+ H

) ≈ 6.3 Oe). For the same film, its EA hysteresis loop in Fig. 3.18(b) shows that the saturation magnetization (4 πM

≈ 15.8 KG), (SQR)

= 0.99, and coercivity (H

≈ 13.8 Oe). Here, it is interesting to note that since H

≦ H

for all the films, they may be classified as the “inverted” films[31]. A brief summary is listed below:

as x or y increases from 0 to 26, 4 πM

remains almost constant, 16.8–15.8 KG, and H

decreases, 34.4–13.8 Oe, and the reasons would be discussed in next

.

0 50 100 150 200

3.10 Magnetostrictions

4. Results and discussion for films

4.1 XRD data

4.2 FMR data

Fe ₅₉ Ni ₂₂ Ga ₁₉ /glass 100nm

( ^∆H ) _exp =133.90 Oe