Temperature evolution of magnetic properties for (Cu/Co)60/Fe ...

Journal of Magnetism and Magnetic Materials 373 (2015) 144–150

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Temperature evolution of magnetic properties for (Cu/Co)60/Fe multilayer O. Yalçın a,n, Ş. Ünlüer b, S. Kazan c, M. Özdemir d, Y. Öner e a

Department of Physics, Niğde University, 51240 Niğde, Turkey Institute of Sciences, Niğde University, 51240 Niğde, Turkey c Department of Physics, Gebze Institute of Technology, Kocaeli, 41400, Turkey d Marmara University, Faculty of Science and Letters, Department of Physics, 34722 Istanbul, Turkey e Department of Physics Engineering, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey b

art ic l e i nf o

a b s t r a c t

Article history: Received 19 February 2014 Received in revised form 7 April 2014 Accepted 14 April 2014 Available online 19 April 2014

In order to investigate the magnetic properties by ferromagnetic resonance (FMR) techniques, (Cu/Co)60/ Fe multilayer on Si(001) substrate has been prepared by conventional sputtering. Evolution of the FMR spectra with temperature, resonance field, and magnetization curve has been calculated using the Landau–Lifshitz equation of motion for magnetization with the Bloch–Bloembergen type damping term. An almost linear evolution of frequency of resonance field has been shown for x-, k- and q-band spectra. By the analysis of the resonance field–frequency relation, the effect of the internal field is refined and thus the spectroscopic g-value and internal field were calculated. The magnetostatic signal originated from the magnetostatic anisotropy energy has been determined to be opposed by the decreasing exchange and dipolar energies. & 2014 Elsevier B.V. All rights reserved.

Keywords: Multilayer film Low temperature FMR study Magnetic property Magnetostatic anisotropy energy Spin–orbit interaction

1. Introduction The interest in smart magnetic multilayers and their applications are driving rapid growth in nanostructures [1–7]. Surface anisotropy in the thin films, sources of the interface anisotropy in Fe/Cu multilayer and the spontaneous magnetization are revealed by thermal behavior [8–10]. Magnetic properties of some multilayers have been studied at room temperature (RT) [11,12]. Different types of techniques such as combinatorial sputter– deposition system [13] and rf sputtering [14] were used to prepare magnetic multilayers [15–20]. FMR study of exchange and dipolar interactions was reported for discontinuous multilayer [21,22]. The competition between interlayer–interfacial exchange couplings and temperature evolution of the static–dynamic magnetic properties of AF/F/AF multilayers and magnetic films was investigated [23–26]. The FMR technique is a powerful technique for studying the spin structure, magnetic properties in bulk samples, thin films, anisotropies, the damping constant, g-factor, spin relaxation, multilayers, nanoparticles, medical and military applications [27–45]. The FMR spectra of the sample depend on the crystal structure and other magnetic properties of material. Magnetic properties of multilayers were analyzed by using the giant

magnetoresistance (GMR) [46–49], vibrating-sample magnetometer (VSM) [50–55], x-ray diffraction (XRD) [56], superconducting quantum interference device (SQUID) magnetometer [57,58], DC magnetron sputtering [59], magneto–optic Kerr effect (MOKE) [60], and Brillouin light scattering (BLS) [61]. The frequency relation of resonance field for nanoscale thin films, granular films [62] and multilayers has been observed by x-, k-, q-, u- and v-band FMR spectra [63–65]. The spectrum of excitations in (Fe/Cr)n structures with a non-collinear magnetic ordering was studied by means of the FMR technique [66]. The FMR modes are worked out for the case of exchange coupled bilayer thin films where the anisotropy axis in the ferromagnetic film is tilted out of the plane [67]. In the scope of this work, we have studied low temperature ferromagnetic resonance , and temperature dependence of (Co/Cu/ Co)/Fe/Si multilayer structure by using the Quantum Design vibrating sample magnetometer model 6000 at RT and low temperatures. Temperature evolution of magnetic moment at field cooling (FC) and zero fields cooling (ZFC) has been studied in detail. Temperature evolution of the symmetrically shaped hysteresis loops and FMR spectra have been studied in detail. Frequency evolution of the FMR resonance field has been analyzed.

2. Experimental procedure n

Corresponding author. Tel.: þ 90 388 225 4068. E-mail addresses: [email protected], [email protected] (O. Yalçın).

http://dx.doi.org/10.1016/j.jmmm.2014.04.033 0304-8853/& 2014 Elsevier B.V. All rights reserved.

The 60
(Co/Cu) multilayer was prepared in a ultrahigh vacuum (UHV) sputtering system. The individual Co and Cu layer

O. Yalçın et al. / Journal of Magnetism and Magnetic Materials 373 (2015) 144–150

thicknesses are about 19 Å and 9 Å respectively. The 60
(Co 19 Å/ Cu 9 Å) multilayer is referred to as (Co/Cu/Co) sandwiches structure. Base pressure of the UHV chamber is 10  10 Torr. The (Cu/ Co)60/Fe sample was deposited on chemically etched Si(100) substrates at a temperature close to 275 K. A thin Fe layer (50 Å) was deposited as a buffer layer on Si(001) substrate. Temperature evolution of the magnetic hysteresis curves and magnetization of the 60
(Co 19 Å/Cu 9 Å) multilayer were performed using the Quantum Design vibrating sample magnetometer (VSM) model 6000. From these results, magnetic parameters such as saturation field, coercive field, remanent magnetization and saturation magnetization have been determined. A set of electron spin resonance (ESR) spectrometer equipped by an electromagnet which provides a dc-magnetic field up to 22 kG in the horizontal plane Bruker EMX type cavities in the temperature range 2–278 K and frequency range 9.5–37 GHz were taken as the magnetic field derivatives of FMR signals. An Oxford Instruments continuous helium-gas flow cryostat was used for cooling. The temperature was controlled by a commercial Lake Shore 340 temperature-control system. Magnetic field evolution of the FMR spectra was taken by a high sensitive conventional x-band (  9.5 GHz), k-band (20–27 GHz), and q-band (30–37 GHz) spectrometer at RT. A goniometer was used to rotate the sample around the sample holder cryostat tube. The angular dependence of the FMR spectra was studied by varying the direction of the external magnetic field with respect to the film plane, both in the sample planes (in-plane-geometry, IPG) and away from sample plane towards the film normal (out-of-plane-geometry, OPG).The external field derivative of microwave power absorption, dP/dH, was registered as a function of the magnetic field H. IPG angular studies of any remarkable anisotropic behavior are not shown in this sample. In other words, for the OPG FMR measurements, the sample was attached to a flat platform which was cut with the normal perpendicular to the sample holder. Upon rotation of the sample holder, the microwave component of the field remained always in the sample plane, whereas the dc field was rotated from the sample plane toward the film normal.

3. Theoretical calculation The coordinate system of the multilayer sample geometry, dc! component of external magnetic field H and relative orientation ! of M as well as the geometric factors are shown in Fig. 1. The total free energy for system can be written as follows: E ¼ EZ þ EB þES !! EZ ¼  M : H ¼  MH ð sin θ sin θH þ cos θ cos θH cos ∅Þ ð1Þ

where EZ, EB and ES are the Zeeman energy, bulk anisotropy and ! surface anisotropy terms respectively. H is the external field and ! M is magnetization vector. In addition, (θH, ∅H ) and (θ; ∅) are ! ! angles in spherical coordinates for H and M . K S1 and Keff are the surface and effective bulk anisotropy constants respectively. The ! equilibrium values of the M are obtained from static equilibrium conditions as follows: ∂E ¼ 0; ∂θ Eθ ¼ MH½ cos θ sin θH cos ð∅ ∅H Þ  sin θ cos θH 

Eθ ¼

 K eff sin 2 θ ¼ 0

Fig. 1. Sketch of the sample geometry of the multilayer system and relative ! orientations of the equilibrium magnetization M and the dc-component of applied ! magnetic field H for the ferromagnetic resonance experiment.

We choose ∅  ∅H ¼ 0 for 60
(Co19 Å/Cu 9 Å) multilayer on Si (001) substrate. Eq. (2) can be easily written as MH½ cos θ sin θH  sin θ cos θH  þ 2πM 2 sin 2θ ¼ 0: Using the Landau–Lifshitz dynamic equation of motion for the magnetization with the Bloch–Bloembergen type damping term can be written as follows: ! ! ! 1 dM ! M θ;∅ M z  M ¼ ∇ E  γ dt T1 T2

ð3Þ

where γ is the gyromagnetic ratio for the films, T2 is the spin–spin relaxation time, T1 is the spin–lattice relaxation time, and ! ^ þð1= sin θÞ ð∂E=∂∅Þθ^ is the torque given by ∇ E ¼  ð∂E=∂θÞ∅ energy density E in the spherical coordinates. The resonance field values as a function of applied field angles have been calculated from the following dispersion relation given by Eq. (3):  2 ω0 ¼ ½H cos ðθ  θH Þ þ H eff cos 2θ γ 

EB ¼ K eff cos 2 θ ES ¼ K S1 cos 2 θ

145

ð2Þ


½H cos ðθ  θH Þ þ H eff cos 2 θ þ

1 γT 2

2 :

ð4Þ

Here, ðω0 =γÞ ¼ gμB H and ω0 is the Larmor frequency of the magnetization in the external dc-effective magnetic field and H eff ¼ ð2K 1 =MÞ  4πM is the effective anisotropy term. The values for total magnetization have been obtained by fitting Heff with experimental results of FMR measurements at different angles (θH) ! of the applied field H . The experimental FMR signals are proportional to the derivative of the absorbed power with respect to the applied field which is also proportional to the imaginary part of the magnetic susceptibility. The theoretical absorption (FMR signals) curves are obtained by using the dχ 2 =dH as a function of external field [28] χ ¼ χ 1 þ iχ 2

4πM s ðEθθ =M s Þ½ðω0 =γÞ2  ðω=γÞ2 þ ið2ω=γ 2 T 2 Þ : ½ðω0 =γÞ2  ðω=γÞ2 2 þ ð2ω=γ 2 T 2 Þ2

ð5Þ

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In the literature, there are standard phenomenological theories and resulting equations to analyze the line width characteristics of the FMR spectra.

4. Result and discussion Temperature evolution of the magnetization is shown in Fig. 2. The magnetization curves are plotted for 1 T (FC) and 0.02 T (FC, ZFC) using the experimental data. The changes in the magnetization with increasing temperature point out an interesting aspect of the different values at different applied fields. The measured magnetization curves for FC slowly decrease with increase in temperature from 0 to  350 K. On the contrary, the experimental magnetization curve for ZFC increases with temperature. In other

words, the magnetization in ZFC regime decreases owing to freezing of magnetic moments of the sample at TB. The magnetization curves for FC and ZFC unite at the blocking temperature (TB,  350 K). Theoretical magnetization curve (dot line in Fig. 2) has been calculated by using the Brillouin function with J¼ 1/2 and g¼ 3.33. This g-value is greater than the free electron g-factor. Therefore, great g-value reminds us of the spin–orbit interaction (see Fig. 8b for detail and comparison). When the magnetization value is zero, temperature corresponds to the Curie temperature (TC). This property of magnetization denotes ferromagnetic regime below TC as shown in Fig. 2. TC was estimated to be nearly 1250 K using the theoretical fitting. This slowly decreases indicating that the 60
(Co19 Å/Cu 9 Å) multilayer is stable in the temperature range of 0–350 K. Fig. 3 shows the evolution of the hysteresis loops for some selected temperature. It is evident from Fig. 3 that hysteresis loops expand with decreasing temperature starting from 350 up to 5 K. Hysteresis loops were recorded for FC at 1 T in this work. The phenomenon of hysteresis in (Cu/Co)60/Fe multilayer at 350 K is called paramagnetic curve. Obviously, all hysteresis loops have a good symmetric shape according to the zero magnetic fields for all temperatures. The temperature dependent measurements show

Fig. 2. Temperature evolution of the normalized magnetization with 1 T (FC, black line) and 0.02 T (FC, ZFC, red line). The dot line curve represents the theoretical fitting. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Evolution of hysteresis loops with temperature.

Fig. 4. Temperature evolution of the saturation field (Hs), coercive field (Hc), remanent magnetization (Mr) and saturation magnetization (Ms).

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that the saturation field (Hs), coercive field (Hc), remanent magnetization (Mr) and the saturation magnetization (Ms) decrease with increasing temperature. Therefore, the expansion in the loops can be attributed to the formation of crystalline phases. It is due to anisotropy that increases as temperature decreases. In additional, the increasing in coercivity may not only be a reason of magnetocrystalline anisotropy but also it may originate from exchange anisotropy due to spin disorder at the film surface at low temperatures (5 K for this study). Evolutions of Hs, Hc, Mr and Ms with temperature are shown in detail in Fig. 4. Temperature evolutions of the saturation field (Hs) and coercive field (Hc) are shown in Fig. 4a and b, respectively. Hs and Hc exponentially increase with decreasing temperature. Behaviors of Hs and Hc according to temperature evolution are nearly similar. Hs and Hc get the lowest values at 350 K. The coercive field has been fitted to Kneller's law (Hc(T)¼ Hc(0 K)(1 (T/TB)1/2), with fitting parameters Hc(0 K) ¼11 70.02 Oe, and TB ¼350705 as shown in Fig. 4b. The experimental and theoretical coercive field values are in good agreement as well. The effective exchange anisotropy prevents the magnetization reversal, so a notable increase is observed in the coercive field (Hc) at low temperatures.

Fig. 5. (a) Temperature dependence of the x-band FMR spectra and their theoretical calculation by Eq. (5) in perpendicular and parallel positions for multilayer structures for some selected temperature with decreasing temperatures. (b) FMR resonance field evolution in perpendicular and parallel position from room to low temperature.

147

Fig. 4c and d represents evolution of the remanent magnetization (Mr) and saturation magnetization (Ms) with temperature. Mr and Ms logarithmically decrease with increasing temperature. Temperature evolutions of Mr and Ms exhibit similar behavior. The decrease in Mr and Ms is slow between the temperatures 5 and 50 K; rapid change occurs between 50 and 350 K. In addition, there is some anomaly at temperature near 5 K. In this work, the spin-valve behavior is not observed clearly. But this behavior shows a tendency to spin-valve behavior at low temperature ( 5 K). Temperature evolution of the magnetization for T o0.5TC for most of the bulk materials may be described by Bloch's law as follows: ~ 3=2 Þ M s ðTÞ ¼ M s ð0Þð1  BT

ð6Þ

where B~ is the spin-wave Bloch parameter. This parameter is in units of K  3/2. It has been shown that an “effective T3/2 law” is valid for two dimensional systems [11]. A bulk-like T3/2 temperature dependence on the magnetization is observed for multilayer structures in the temperature range 5–300 K [9]. The saturation magnetization (Ms) has been fitted to Bloch's law in Eq. (6) with fitting parameters Ms(0 K) ¼1700 720 emu/cm3, and B~ ¼ (4.770.1)
10  5 K  3/2) as shown in Fig. 4d. The theoretical and

Fig. 6. (a) Temperature evolution of the perpendicular experimental FMR spectra and their theoretical signals, (b) theoretical calculation of the temperature dependence of surface anisotropy constant.

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Fig. 7. (a) Angular dependence of the x- band FMR spectra at 278 K, (b) resonance field values and their theoretical calculation value at 278 K, (c) angular dependence of the FMR spectra at 35 K, (d) resonance field values and their theoretical calculation value at 35 K for (Cu/Co)60/Fe sample on Si(001) substrate.

experimental saturation magnetizations are in good agreement as well. Fig. 5a illustrates temperature evolution of the FMR spectra from near the RT ( 278 K) to low temperatures (  35 K and 2 K) at parallel and perpendicular positions, respectively. A single and relatively narrow FMR signal was seen at low magnetic fields in the parallel direction. The resonance field did not show any remarkable changes in the temperature range 278–35 K in parallel position. This behavior originates from crystalline situation for this sample. On the contrary, the FMR spectra were shown as two and three signals in perpendicular position at 273 and 35–2 K, respectively. On the other hand, two FMR spectra at the perpendicular position are divided into three signals (main mode (MM), surface mode (SM) and magnetostatic (MgM), respectively) at low temperatures (  35 K and 2 K) [labeled by Hr1, Hr2, and Hr3, Fig. 5a]. In other words, the two low-field FMR signal overlapped and merged in the single FMR peak at RT. The out-of-plane anisotropy of MM (Hr1), SM (Hr2) and MgM (Hr3) is a typical feature of thin multilayer films [2,3,29]. This anisotropy is so called shape anisotropy. The magnetostatic mode is reflected in the exchange effects between Co and Fe layers at low temperature (see the text of Fig. 7 for detail). The FMR signal at high field has a narrow line-width and high intensity in temperature range 194–2 K at perpendicular position. This smaller linewidth at high temperature is due to the smaller effective anisotropy. The high-field signal (in Fig. 5a) is shifted gradually to higher fields with decreasing temperature at perpendicular position. This means that the magnetic easy axis is parallel to the film plane. Evolutions of the resonance fields with temperature are shown in Fig. 5b for parallel and perpendicular direction in detail. The dramatic enhancement of resonance field near 70 K for MM and the initial reduction of the resonance field from room to low temperature are shown in perpendicular position (Fig. 5b). Temperature evolution of the resonance field is due to the effective thickness or more significantly due to the surface area to volume

ratio. This property is related to surface anisotropy. These type behaviors are seen in detail for other thin film structures. Our result for (Cu/Co)60/Fe sample on Si(001) substrate near the 70 K is compatible with previous studies [36,41,68–70]. Evolution of the perpendicular experimental FMR spectra and their theoretical spectra with temperature are shown in Fig. 6a. The theoretical and experimental FMR spectra are in good agreement as well. The first peak near the 18 kG and second one near the 23 kG originate from the Co and Fe layers, respectively. From this figure, the FMR spectra in perpendicular position are quite symmetric with respect to the resonance field values near the room temperature. The FMR signal for Co layers apparently contains two coupled peaks at low temperature region (see Fig. 5a for two coupled peaks at low temperature). The second peak in the two coupled peaks at 18 kG arises from the exchange effects between Co and Fe layers or at the surface region of Co layers. The temperature dependence of surface anisotropy constant has been calculated from the theoretical analysis (Eq. (4) and K1 in Heff) as shown in Fig. 6b. The surface anisotropy constant linearly increases with decreasing temperature from 273 to 105 K. Angular dependence of the FMR spectra at some selected degree in OPG and their resonance field values with theoretical calculation (Eq. (4)) for (Cu/Co)60/Fe multilayer have been observed in Fig. 7a–d at 278 and 35 K, respectively. There is no in-plane anisotropic behavior for FMR spectra at both temperatures. The FMR spectra at both temperatures are strongly angular dependent. The signal in the film-plane and out of plane geometry contains one and two resonance peaks (with MgM mode) that arise at the field above 0.805 kG and 18 kG at 278 and 35 K, respectively. As can be seen from Fig. 7a and c, FMR signals at IPG are near symmetric with respect to the resonance field values for both temperatures. In additional, line widths at IPG are significantly narrower compared to line widths at OPG. Line width expands from parallel to near 85 degree. Because the FMR signal contains two peaks, the peak-to-peak line width of the spectra

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149

near the perpendicular directions (86–90 degrees) is very narrow according to the line width for middle angles. The narrow peak-topeak line width of the FMR spectra is related to the high quality of the sample. In the spectra for parallel position the overlap of the three signals (MM, SM, MgM) makes their individual analysis difficult at 35 K. The spectra at perpendicular position are better resolved according to the spectra at parallel position. The theoretical analysis (by Eq. (4)) revealed that the peak at lower field belongs to main absorption of Co layers, while the other peak at high field is Fe layer or surface mode excited at low temperature (105 K in Fig. 6a). As the temperature is lowered, the signal near the 19.2 kG splits into two different peaks. The third peak (magnetostatic mode, MgM) near the 19.2 kG arises from the exchange effects between Co and Fe layers or at the surface region of Co layers at 35 K. This behavior is originated from the magnetostatic anisotropy effects [29]. The angular evolution of both experimental and fitted values (by Eq. (4)) for resonance field has been shown in Fig. 7b and d at 278 and 35 K, respectively. As seen in this figure, the resonance fields exhibit very strong anisotropic behavior for OPG position. In fact, the periodicity of resonance fields for both temperatures is exactly 180 degree. The resonance field variation increases when temperature decreases near 90 degree. Theoretical calculation of resonance field values has been obtained by computer modeling based on the theory given above with Eq. (4). The experimental and theoretical resonance field values are in good agreement as well at high and low temperatures. The theoretical analysis on the FMR resonance field was carried out and the magnetic parameters have been obtained according to the dispersion relation (Eq. (4)) using the equation of motion for magnetization with Bloch– Bloembergen type damping term (T2 ¼(1 70.5)
10-6 s). The resonance field value near the 19.2 kG is related to the magnetostatic anisotropy effects. The frequency evolution of FMR spectra in k- and q-bands was performed at room temperature as shown in Fig. 8a. As can be seen from this figure, while microwave frequency increases, FMR resonance field of spectra increases. A typical experimental frequency dependence of FMR resonance field in x-, k-, and q-bands at RT, together with the theoretical calculations, is shown in Fig. 8b. There is an almost linear relation between the resonance field and microwave frequency. Frequency evolution of the resonance field values, such any broad band indicates that magnetic susceptibility is very low. As the curve extrapolated to lower frequency (9.5 GHz, green full circle), it cuts the horizontal line at non-zero value. This curve is fitted to the expression hγ¼ gβ (Hr þ Hi). Here h, γ, g, β, Hr, and Hi are the Planck's constant, microwave frequency, spectroscopic splitting factor, Bohr magneton, FMR resonance field value and internal magnetic field respectively. Hi and g-values were deduced by fitting the experimental resonance field to the above expression. A significant value of Hi is calculated as 1483 G. The effective g-value of (Cu/Co)60/Fe multilayer is calculated from the slope of curve and found as g ¼3.33. The g-factor is directly related to the ratio of the orbital and spin moment [28,71]. In consideration of the spin–orbit interaction, part of the orbital moment can be pulled in the spin direction. If this interaction prefers the spin and orbit to be parallel to each other, the total magnetic moment will only be greater than part of the spinel side and so g-factor will be greater than free electron g-value 2.0023.

analyzed in detail. The FMR spectra are strongly angular dependent for OPG at 278 and 35 K. The film contains two and three signals at 278 and 35 K, respectively. The low and high field peaks belong to main absorption (MM) of Co- and Fe-bilayer/surface mode (SM) at 35 K. The additional peak between MM and SM corresponds to magnetostatic mode (MgM). The MgM originates from the magnetostatic anisotropy energy dependence of thermal energy. In other words, the MgM is opposed by the decreasing exchange and dipolar energies. The MgM is generally seen in the spin-wave regime of temperature. The small exchange interaction because of nonmagnetic Cu spacer is weak compared to the magnetocrystalline anisotropy [30]. The anisotropy of a multilayer structure remains nearly constant with the number of bilayer repeats [40]. But the spin–orbit interaction is the primary origin of magnetocrystalline anisotropy in this work. The effective g-value

5. Conclusions

Fig. 8. (a) The frequency evolution of the FMR spectra at RT in k-and q-bands. (b) Frequency evolution of the resonance field values in the frequency range of 9.5–36 GHz. The full circle and full lines are experimental results from x-, k-, and q-bands FMR data and theoretical calculations, respectively. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

Evolution of the FMR spectra, saturation field, coercivity, remanent magnetization, saturation magnetization, resonance field and surface anisotropy constant with temperature has been

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(g ¼3.33) for (Cu/Co)60/Fe sample on Si(001) substrate is greater than the free electron g-value (2.0023). This g-factor is directly related to the ratio of the orbital and spin moment. In consideration of the spin–orbit interaction, part of the orbital moment can be pulled in the spin orientation. If the spin–orbit interaction prefers the spin and orbit to be parallel to each other, the total magnetic moment of the film will be only greater than part of the spinel side and so g-value for (Cu/Co)60/Fe sample will be greater than free electron g-value. The experimental FMR spectra, angular dependence of resonance field, frequency relation of resonance field and their theoretical calculations are in good agreement as well in this study.

Acknowledgments We would like to thank Professor A. Fert for his kindness to provide the sample. This study was supported by research fund (Grant no. FEB2012/03) from Niğde University. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

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