**3.2 Magnetic properties**

**Figure 2** shows the static magnetization of Ta (25)/FeGaB (t)/Ta (5). Magnetic moments have been increasing with increasing thickness of FeGaB. This means that magnetic spins of FeGaB are aligned along the easy axis. The magnetic coercive field (Hc) and squareness (Mr/Ms) have measured for the thickness of FeGaB film as shown in **Figure 2b**. As the thickness of film increases, Hc has initially decreased, in a while gradually increased. At film thickness, 25 nm has shown the low value of Hc

#### **Figure 1**

*(a) The RMS values versus of thickness of FeGaB layer of thin film stack Ta (25)/FeGaB (15, 25, 50, and 75)/Ta (5); inset display the 3D image of thin films Ta (25)/FeGaB (75)/Ta (5). (b) AFM image of Ta (25)/FeGaB (15)/ Ta (5).*

#### **Figure 2.**

*(a) M-H loop of Ta (25)/FeGaB (t)/Ta (5) (b) coercive field (Hc) and squareness (Mr/Ms) of Ta (25)/FeGaB (t)/Ta versus thickness of FeGaB.*

#### **Figure 3.**

*(a) inhomogeneous of line width (*∆*H0) as a function of temperature (b) damping factor (α) versus temperature (T(K)) for Ta (25)/FeGaB (t)/Ta (5).*

and squareness, due to the influence of the buffer layer on magnetic spins of FGB. The large value of Hc has been obtained for the 75 nm thickness of FGB.

#### **3.3 Dynamic properties**

**Figure 3a** and **b** shows the inhomogeneous of line width (∆H0) and damping factor (α) as a function of temperature. The ∆H0 and *α* have been derived from the resonance line width (∆H) – excitation frequency (GHz) by fitting ∆H = ∆H0 + αf/γ [34, 35]. The thickness of FGB thin film increases, the (∆H0) is increasing at a specific temperature. The large thickness of FGB thin film (75 nm) has shown a large value of the ∆H0 among all thin films. The temperature lowering to 100 K from 300 K, ∆H0 is decreasing for FGB thin film thickness of 15–50 nm. Whereas, the 75 nm thickness of FGB thin film has shown an increasing trend, due to the creation of defects or structural imperfections for lowering the temperature.

**Figure 3b** shows the damping factor (α) as a function of temperature. The α has increased for lowering the temperature, except for the 75 nm thin film of FGB. The thickness of 50 nm FGB has shown a large damping value at 100 K. Because the 50 nm of FGB thin films shown a low value of ∆H0 at 100 K. It means that the thin film has not produced any defects/structural imperfection, otherwise condensed the defects.

*Spin Pumping in Magnetostrictive Ta/FeGaB/Ta Multilayer Thin Films DOI: http://dx.doi.org/10.5772/intechopen.106183*

**Figure 4.**

*(a) The thickness dependence of damping fitted with linearly to obtain surface/ inherent damping (α0) and interface damping (αi) (b) the plot of the obtained α0 and αi temperature.*

Therefore, the damping factor of the spin-wave is increasing for a 50 nm thin film of FGB. Whereas, 75 nm thickness FGB has exhibited a low value of damping due to multiple scattering of spin-wave from the defect and imperfections.

To find out interface and surface damping, damping factor (α) multiply with the thickness of FGB film and plotted with the thickness of FGB as shown in **Figure 4a**. The plot (αt vs. t) is linearly fitted an obtained the surface or inherent damping (α0) and interface damping (αi) parameters [35]. These parameters are varying for different temperatures. The surface damping is initially increasing for 300–250 K as shown in **Figure 4b**, later on, it is decreasing for lowering the temperature. Whereas the interface damping is exhibiting the opposite nature to surface damping. Finally, we can conclude that surface damping is mostly dominant at near to RT, and interface damping is dominant at a lower temperature in this film stack.

The effective magnetization has been found out from Kettle equation [35–37] fitted with frequency-resonance magnetic fields spectrum. Magnetic anisotropy (Hk) has been found along with effective magnetization, which shows a positive value and small value compare to effective magnetization. It means that no perpendicular anisotropy generates at the interface. Therefore, the effective magnetization is considering as surface magnetization (Ms). The parameter Ms. has been utilized for further calculation.

#### **3.4 Spin pumping at the interface of Ta/ FGB**

The spin pumping associate with the real part of the spin-mixing conductance (geff). The g parameter is proportional to the flux of angular momentum in the form of spin-polarized carriers the ferromagnet/nonmagnetic interface. This is seen by gyromagnetic precession in a ferromagnet. The enhanced damping factor has been found out by the subtraction of damping factor (α), inherent/surface damping (α0). The inherent/surface, interface damping obtained from the plotting of dampingthickness of FGB as shown in **Figure 4b**. The enhanced damping is related to spinmixing conductance and thickness of FGB [7, 11, 12, 38, 39].

$$
\Delta\alpha = \alpha - \alpha\_o = \text{g}\,\mu\_o \frac{\text{g}\_{\text{eff}}}{4\pi \,\text{Mst}\_{\text{FG}}} \tag{1}
$$

where g is Lande factor, μB is Bohr constant, Ms is saturation magnetization and tFGB is the thickness of FeGaB magnetic film.

#### **Figure 5.**

*(a) thickness depended on 4π × (α−α0) × Ms × t at different temperature 300–100 K for calculating the spin mixing conductance (geff) at the interface, (b) At 200 K, a linear fit of thickness depended on 4π × (α−α0) × Ms × t provided the geff as 0.0962 × 1018 m−2.*

#### **Figure 6.**

*(a) spin mixing conductance (geff) as a function of temperature (T (K), (b) shows the linear fit of geff-T plot, the intercept of the plot provides spin mixing conductance at 0 K.*

To investigate the spin mixing conductance (geff), the enhanced damping factor has multiplied with saturation magnetization and thickness of magnetic films FeGaB. The product term has plotted with the thickness of FGB thin film, as shown in **Figure 5a**. The extraction of the spin mixing conductance (geff) has been obtained by linear fit as shown in **Figure 5b**. The mixing conductance value of the Ta/FeGaB/Ta thin film stack is 0.082 × 1018 m−2 at 300 K, which has been increased gradually with lower temperature, as shown in **Figure 6**. This values are comparable with Si/SiO/Ta/Co(t)/ Cu/Ta [40, 41], the Co/Cu films has mixing conductance 0.41 × 1018 m−2. The conductance order is the same value; magnitude is different values. FeGaB thin film has a lower magnitude than that of the Co(t)/Cu. We can understand that spin pumping at the interface has reduced, due to the large thickness of FeGaB films and the large value of magnetostriction constant FeGaB.

**Figure 6a** shows the spin mixing conductance as a function of temperature. The mixing conductance has enhanced for lowering the temperature. At 100 K, the mixing conductance is a large value, 0.1245 × 1018 m−2. It means that spin diffusion at the interface of Ta and FeGaB is increasing for low temperatures. We can conclude that spin mixing conductance depends on temperature. The linear fit of mixing conductance provides OK spin mixing conductance, as shown in **Figure 6b**. This value is 0.1417 × 1018 m−2.
