following expression \[29\]:

$$\label{equation5}
    \Delta H = \Delta H_0 +\frac{4 \pi \alpha \it{f}}{\gamma}$$

where **$\Delta H_0$** is the inhomogeneous broadening of linewidth which depends on the homogeneity of the sample. There are various other effects such as interface effect, impurity, magnetic proximity effects (MPE) etc., which also can enhance the value of $\alpha$ of the system. Hence, the total $\alpha$ can be written as: $$\label{q6}
    \alpha = \alpha_{int} + \alpha_{impurity} + \alpha_{MPE} + \alpha_{sp}$$

where $\alpha_{int}$ is the intrinsic damping, and $\alpha_{impurity}$, $\alpha_{MPE}$, and $\alpha_{sp}$ are the contribution from impurity, magnetic proximity effect (MPE), and spin pumping to the $\alpha$, respectively \[30\].

![(a) $\textit{f}$ vs $H_r$ and (b) $\Delta H$ vs $\textit{f}$ plots for the samples S1 (open squares) and S5 (open circles). The solid lines are the best fits which are fitted by equations \[equation3\] and \[equation5\]. []{data-label="fig2"}](fig2.png){width="45.00000%"}

The linear behaviour of *$\Delta H$* vs $\textit{f}$ plots implies the good homogeneity in our samples and it rules out the possibility of any kind of magnetic impurity of the FM layer.

   S1   0.0066 $\pm$ 0.0001
  ---- ---------------------
   S2   0.0063 $\pm$ 0.0001
   S3   0.0070 $\pm$ 0.0001
   S4   0.0085 $\pm$ 0.0001
   S5   0.0087 $\pm$ 0.0001

  : The values of $\alpha$ for samples 